\documentclass[12pt]{article} \usepackage{tikz} \usepackage{amsmath} % Underlining package \usepackage{ulem} \usetikzlibrary{calc} \usetikzlibrary{angles,quotes} \usetikzlibrary{decorations.markings, arrows.meta} \usepackage[a4paper, portrait, margin=1cm]{geometry} \usepackage{fancyhdr} \newcommand{\HeadingAnswers}{% \section*{\Large Name: \underline{\hspace{8cm}} \hfill Date: \underline{\hspace{3cm}}}% \vspace{-3mm}\par \textbf{Area Rectangles: Answers}\vspace{1pt}\hrule } % raise footer with page number; no header \fancypagestyle{myfancypagestyle}{ \fancyhf{}% clear all header and footer fields \renewcommand{\headrulewidth}{0pt} % no rule under header \fancyfoot[C] {\thepage} \setlength{\footskip}{14.5pt} % raise page number allowed min 14.5pt } \pagestyle{myfancypagestyle} % apply myfancypagestyle \newcounter{minipagecount} \begin{document} \HeadingAnswers \vspace{8mm} \begin{minipage}{0.55\textwidth} \refstepcounter{minipagecount} \noindent{(\theminipagecount)}\quad \begin{tikzpicture}[scale=1.0, baseline=(current bounding box.north)] \begin{scope}[rotate=0] \coordinate (P) at (0,0); \coordinate (Q) at (1.716,0); \coordinate (T) at ($(Q)+(0.867,0)$); % extend out \coordinate (R) at ($(Q)+(0.867,1.525)$); % Perpendicular upwards \coordinate (S) at ($(P)+(0.867,1.525)$); % Perpendicular upwards \draw (P)--(Q)--(R)--(S)--cycle; \draw[dashed] (Q)--(T); \draw[dashed] (T)--(R); \pic [draw, -, angle radius=0.2cm] {right angle=Q--T--R}; \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>>}}}] (P)--(Q); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>>}}}] (S)--(R); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>}}}] (Q)--(R); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>}}}] (P)--(S); % Vertex LABELS % Labels relative to shape geometry \node at ($(P)+(-0.2,-0.2)$) {P}; \node at ($(Q)+(0.0,-0.2)$) {Q}; \node at ($(T)+(0.2,-0.2)$) {T}; \node at ($(R)+(0.2,0.2)$) {R}; \node at ($(S)+(-0.2,0.2)$) {S}; % dotted/dashed arrows shifted away from edges % Horizontal side (A-B), shifted down yshift=0mm, \draw[<->, gray] ($(P) + (0,-0.7cm)$) -- ($(Q) + (0,-0.7cm)$) node[black, midway, fill=white, inner sep=2.5pt] {9\,cm}; % Vertical side (D-C), shifted right xshift=0mm, \draw[<->, gray] ($(T)+(0.6,0)$) -- ($(T |- R)+(0.6,0)$) node[black, midway, fill=white, inner sep=2.5pt] {8\,cm}; \end{scope} \end{tikzpicture} \end{minipage}% \hfill \begin{minipage}{.4\textwidth} \begin{align*} \text{Area} &= \text{bh} \\ \text{Area} &= 9 \text{cm} \times 8 \text{cm} \\ \text{Area} &= 72 \text{cm}^2 \end{align*} \end{minipage} \par\vspace{1cm}\begin{minipage}{0.55\textwidth} \refstepcounter{minipagecount} \noindent{(\theminipagecount)}\quad \begin{tikzpicture}[scale=1.0, baseline=(current bounding box.north)] \begin{scope}[rotate=270] \coordinate (K) at (0,0); \coordinate (L) at (2.016,0); \coordinate (O) at ($(L)+(1.939,0)$); % extend out \coordinate (M) at ($(L)+(1.939,1.764)$); % Perpendicular upwards \coordinate (N) at ($(K)+(1.939,1.764)$); % Perpendicular upwards \draw (K)--(L)--(M)--(N)--cycle; \draw[dashed] (L)--(O); \draw[dashed] (O)--(M); \pic [draw, -, angle radius=0.2cm] {right angle=L--O--M}; \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>>}}}] (K)--(L); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>>}}}] (N)--(M); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>}}}] (L)--(M); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>}}}] (K)--(N); % Vertex LABELS % Labels relative to shape geometry \node at ($(K)+(-0.2,-0.2)$) {K}; \node at ($(L)+(0.0,-0.2)$) {L}; \node at ($(O)+(0.2,-0.2)$) {O}; \node at ($(M)+(0.2,0.2)$) {M}; \node at ($(N)+(-0.2,0.2)$) {N}; % dotted/dashed arrows shifted away from edges % Horizontal side (A-B), shifted down yshift=0mm, \draw[<->, gray] ($(K) + (0,-0.7cm)$) -- ($(L) + (0,-0.7cm)$) node[black, midway, fill=white, inner sep=2.5pt] {8\,cm}; % Vertical side (D-C), shifted right xshift=0mm, \draw[<->, gray] ($(O)+(0.6,0)$) -- ($(O |- M)+(0.6,0)$) node[black, midway, fill=white, inner sep=2.5pt] {7\,cm}; \end{scope} \end{tikzpicture} \end{minipage}% \hfill \begin{minipage}{.4\textwidth} \begin{align*} \text{Area} &= \text{bh} \\ \text{Area} &= 8 \text{cm} \times 7 \text{cm} \\ \text{Area} &= 56 \text{cm}^2 \end{align*} \end{minipage} \par\vspace{1cm}\begin{minipage}{0.55\textwidth} \refstepcounter{minipagecount} \noindent{(\theminipagecount)}\quad \begin{tikzpicture}[scale=1.0, baseline=(current bounding box.north)] \begin{scope}[rotate=-20] \coordinate (F) at (0,0); \coordinate (G) at (5.814,0); \coordinate (J) at ($(G)+(1.186,0)$); % extend out \coordinate (H) at ($(G)+(1.186,1.292)$); % Perpendicular upwards \coordinate (I) at ($(F)+(1.186,1.292)$); % Perpendicular upwards \draw (F)--(G)--(H)--(I)--cycle; \draw[dashed] (G)--(J); \draw[dashed] (J)--(H); \pic [draw, -, angle radius=0.2cm] {right angle=G--J--H}; \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>>}}}] (F)--(G); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>>}}}] (I)--(H); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>}}}] (G)--(H); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>}}}] (F)--(I); % Vertex LABELS % Labels relative to shape geometry \node at ($(F)+(-0.2,-0.2)$) {F}; \node at ($(G)+(0.0,-0.2)$) {G}; \node at ($(J)+(0.2,-0.2)$) {J}; \node at ($(H)+(0.2,0.2)$) {H}; \node at ($(I)+(-0.2,0.2)$) {I}; % dotted/dashed arrows shifted away from edges % Horizontal side (A-B), shifted down yshift=0mm, \draw[<->, gray] ($(F) + (0,-0.7cm)$) -- ($(G) + (0,-0.7cm)$) node[black, midway, fill=white, inner sep=2.5pt] {9\,cm}; % Vertical side (D-C), shifted right xshift=0mm, \draw[<->, gray] ($(J)+(0.6,0)$) -- ($(J |- H)+(0.6,0)$) node[black, midway, fill=white, inner sep=2.5pt] {2\,cm}; \end{scope} \end{tikzpicture} \end{minipage}% \hfill \begin{minipage}{.4\textwidth} \begin{align*} \text{Area} &= \text{bh} \\ \text{Area} &= 9 \text{cm} \times 2 \text{cm} \\ \text{Area} &= 18 \text{cm}^2 \end{align*} \end{minipage} \par\vspace{1cm}\begin{minipage}{0.55\textwidth} \refstepcounter{minipagecount} \noindent{(\theminipagecount)}\quad \begin{tikzpicture}[scale=1.0, baseline=(current bounding box.north)] \begin{scope}[rotate=180] \coordinate (A) at (0,0); \coordinate (B) at (5.173,0); \coordinate (E) at ($(B)+(1.263,0)$); % extend out \coordinate (C) at ($(B)+(1.263,2.217)$); % Perpendicular upwards \coordinate (D) at ($(A)+(1.263,2.217)$); % Perpendicular upwards \draw (A)--(B)--(C)--(D)--cycle; \draw[dashed] (B)--(E); \draw[dashed] (E)--(C); \pic [draw, -, angle radius=0.2cm] {right angle=B--E--C}; \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>>}}}] (A)--(B); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>>}}}] (D)--(C); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>}}}] (B)--(C); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>}}}] (A)--(D); % Vertex LABELS % Labels relative to shape geometry \node at ($(A)+(-0.2,-0.2)$) {A}; \node at ($(B)+(0.0,-0.2)$) {B}; \node at ($(E)+(0.2,-0.2)$) {E}; \node at ($(C)+(0.2,0.2)$) {C}; \node at ($(D)+(-0.2,0.2)$) {D}; % dotted/dashed arrows shifted away from edges % Horizontal side (A-B), shifted down yshift=0mm, \draw[<->, gray] ($(A) + (0,-0.7cm)$) -- ($(B) + (0,-0.7cm)$) node[black, midway, fill=white, inner sep=2.5pt] {7\,cm}; % Vertical side (D-C), shifted right xshift=0mm, \draw[<->, gray] ($(E)+(0.6,0)$) -- ($(E |- C)+(0.6,0)$) node[black, midway, fill=white, inner sep=2.5pt] {3\,cm}; \end{scope} \end{tikzpicture} \end{minipage}% \hfill \begin{minipage}{.4\textwidth} \begin{align*} \text{Area} &= \text{bh} \\ \text{Area} &= 7 \text{cm} \times 3 \text{cm} \\ \text{Area} &= 21 \text{cm}^2 \end{align*} \end{minipage} \par\vspace{1cm}\begin{minipage}{0.55\textwidth} \refstepcounter{minipagecount} \noindent{(\theminipagecount)}\quad \begin{tikzpicture}[scale=1.0, baseline=(current bounding box.north)] \begin{scope}[rotate=100] \coordinate (K) at (0,0); \coordinate (L) at (2.8,0); \coordinate (O) at ($(L)+(2.434,0)$); % extend out \coordinate (M) at ($(L)+(2.434,2.1)$); % Perpendicular upwards \coordinate (N) at ($(K)+(2.434,2.1)$); % Perpendicular upwards \draw (K)--(L)--(M)--(N)--cycle; \draw[dashed] (L)--(O); \draw[dashed] (O)--(M); \pic [draw, -, angle radius=0.2cm] {right angle=L--O--M}; \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>>}}}] (K)--(L); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>>}}}] (N)--(M); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>}}}] (L)--(M); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>}}}] (K)--(N); % Vertex LABELS % Labels relative to shape geometry \node at ($(K)+(-0.2,-0.2)$) {K}; \node at ($(L)+(0.0,-0.2)$) {L}; \node at ($(O)+(0.2,-0.2)$) {O}; \node at ($(M)+(0.2,0.2)$) {M}; \node at ($(N)+(-0.2,0.2)$) {N}; % dotted/dashed arrows shifted away from edges % Horizontal side (A-B), shifted down yshift=0mm, \draw[<->, gray] ($(K) + (0,-0.7cm)$) -- ($(L) + (0,-0.7cm)$) node[black, midway, fill=white, inner sep=2.5pt] {4\,cm}; % Vertical side (D-C), shifted right xshift=0mm, \draw[<->, gray] ($(O)+(0.6,0)$) -- ($(O |- M)+(0.6,0)$) node[black, midway, fill=white, inner sep=2.5pt] {3\,cm}; \end{scope} \end{tikzpicture} \end{minipage}% \hfill \begin{minipage}{.4\textwidth} \begin{align*} \text{Area} &= \text{bh} \\ \text{Area} &= 4 \text{cm} \times 3 \text{cm} \\ \text{Area} &= 12 \text{cm}^2 \end{align*} \end{minipage} \par\vspace{1cm}\begin{minipage}{0.55\textwidth} \refstepcounter{minipagecount} \noindent{(\theminipagecount)}\quad \begin{tikzpicture}[scale=1.0, baseline=(current bounding box.north)] \begin{scope}[rotate=-30] \coordinate (P) at (0,0); \coordinate (Q) at (2.083,0); \coordinate (T) at ($(Q)+(1.205,0)$); % extend out \coordinate (R) at ($(Q)+(1.205,1.736)$); % Perpendicular upwards \coordinate (S) at ($(P)+(1.205,1.736)$); % Perpendicular upwards \draw (P)--(Q)--(R)--(S)--cycle; \draw[dashed] (Q)--(T); \draw[dashed] (T)--(R); \pic [draw, -, angle radius=0.2cm] {right angle=Q--T--R}; \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>>}}}] (P)--(Q); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>>}}}] (S)--(R); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>}}}] (Q)--(R); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>}}}] (P)--(S); % Vertex LABELS % Labels relative to shape geometry \node at ($(P)+(-0.2,-0.2)$) {P}; \node at ($(Q)+(0.0,-0.2)$) {Q}; \node at ($(T)+(0.2,-0.2)$) {T}; \node at ($(R)+(0.2,0.2)$) {R}; \node at ($(S)+(-0.2,0.2)$) {S}; % dotted/dashed arrows shifted away from edges % Horizontal side (A-B), shifted down yshift=0mm, \draw[<->, gray] ($(P) + (0,-0.7cm)$) -- ($(Q) + (0,-0.7cm)$) node[black, midway, fill=white, inner sep=2.5pt] {6\,cm}; % Vertical side (D-C), shifted right xshift=0mm, \draw[<->, gray] ($(T)+(0.6,0)$) -- ($(T |- R)+(0.6,0)$) node[black, midway, fill=white, inner sep=2.5pt] {5\,cm}; \end{scope} \end{tikzpicture} \end{minipage}% \hfill \begin{minipage}{.4\textwidth} \begin{align*} \text{Area} &= \text{bh} \\ \text{Area} &= 6 \text{cm} \times 5 \text{cm} \\ \text{Area} &= 30 \text{cm}^2 \end{align*} \end{minipage} \par\vspace{1cm}\begin{minipage}{0.55\textwidth} \refstepcounter{minipagecount} \noindent{(\theminipagecount)}\quad \begin{tikzpicture}[scale=1.0, baseline=(current bounding box.north)] \begin{scope}[rotate=-10] \coordinate (F) at (0,0); \coordinate (G) at (4.9,0); \coordinate (J) at ($(G)+(0.694,0)$); % extend out \coordinate (H) at ($(G)+(0.694,2.45)$); % Perpendicular upwards \coordinate (I) at ($(F)+(0.694,2.45)$); % Perpendicular upwards \draw (F)--(G)--(H)--(I)--cycle; \draw[dashed] (G)--(J); \draw[dashed] (J)--(H); \pic [draw, -, angle radius=0.2cm] {right angle=G--J--H}; \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>>}}}] (F)--(G); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>>}}}] (I)--(H); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>}}}] (G)--(H); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>}}}] (F)--(I); % Vertex LABELS % Labels relative to shape geometry \node at ($(F)+(-0.2,-0.2)$) {F}; \node at ($(G)+(0.0,-0.2)$) {G}; \node at ($(J)+(0.2,-0.2)$) {J}; \node at ($(H)+(0.2,0.2)$) {H}; \node at ($(I)+(-0.2,0.2)$) {I}; % dotted/dashed arrows shifted away from edges % Horizontal side (A-B), shifted down yshift=0mm, \draw[<->, gray] ($(F) + (0,-0.7cm)$) -- ($(G) + (0,-0.7cm)$) node[black, midway, fill=white, inner sep=2.5pt] {4\,cm}; % Vertical side (D-C), shifted right xshift=0mm, \draw[<->, gray] ($(J)+(0.6,0)$) -- ($(J |- H)+(0.6,0)$) node[black, midway, fill=white, inner sep=2.5pt] {2\,cm}; \end{scope} \end{tikzpicture} \end{minipage}% \hfill \begin{minipage}{.4\textwidth} \begin{align*} \text{Area} &= \text{bh} \\ \text{Area} &= 4 \text{cm} \times 2 \text{cm} \\ \text{Area} &= 8 \text{cm}^2 \end{align*} \end{minipage} \par\vspace{1cm}\begin{minipage}{0.55\textwidth} \refstepcounter{minipagecount} \noindent{(\theminipagecount)}\quad \begin{tikzpicture}[scale=1.0, baseline=(current bounding box.north)] \begin{scope}[rotate=180] \coordinate (V) at (0,0); \coordinate (W) at (3.302,0); \coordinate (Z) at ($(W)+(2.068,0)$); % extend out \coordinate (X) at ($(W)+(2.068,2.064)$); % Perpendicular upwards \coordinate (Y) at ($(V)+(2.068,2.064)$); % Perpendicular upwards \draw (V)--(W)--(X)--(Y)--cycle; \draw[dashed] (W)--(Z); \draw[dashed] (Z)--(X); \pic [draw, -, angle radius=0.2cm] {right angle=W--Z--X}; \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>>}}}] (V)--(W); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>>}}}] (Y)--(X); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>}}}] (W)--(X); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>}}}] (V)--(Y); % Vertex LABELS % Labels relative to shape geometry \node at ($(V)+(-0.2,-0.2)$) {V}; \node at ($(W)+(0.0,-0.2)$) {W}; \node at ($(Z)+(0.2,-0.2)$) {Z}; \node at ($(X)+(0.2,0.2)$) {X}; \node at ($(Y)+(-0.2,0.2)$) {Y}; % dotted/dashed arrows shifted away from edges % Horizontal side (A-B), shifted down yshift=0mm, \draw[<->, gray] ($(V) + (0,-0.7cm)$) -- ($(W) + (0,-0.7cm)$) node[black, midway, fill=white, inner sep=2.5pt] {8\,cm}; % Vertical side (D-C), shifted right xshift=0mm, \draw[<->, gray] ($(Z)+(0.6,0)$) -- ($(Z |- X)+(0.6,0)$) node[black, midway, fill=white, inner sep=2.5pt] {5\,cm}; \end{scope} \end{tikzpicture} \end{minipage}% \hfill \begin{minipage}{.4\textwidth} \begin{align*} \text{Area} &= \text{bh} \\ \text{Area} &= 8 \text{cm} \times 5 \text{cm} \\ \text{Area} &= 40 \text{cm}^2 \end{align*} \end{minipage} \par\vspace{1cm}\begin{minipage}{0.55\textwidth} \refstepcounter{minipagecount} \noindent{(\theminipagecount)}\quad \begin{tikzpicture}[scale=1.0, baseline=(current bounding box.north)] \begin{scope}[rotate=45] \coordinate (K) at (0,0); \coordinate (L) at (3.766,0); \coordinate (O) at ($(L)+(0.819,0)$); % extend out \coordinate (M) at ($(L)+(0.819,2.092)$); % Perpendicular upwards \coordinate (N) at ($(K)+(0.819,2.092)$); % Perpendicular upwards \draw (K)--(L)--(M)--(N)--cycle; \draw[dashed] (L)--(O); \draw[dashed] (O)--(M); \pic [draw, -, angle radius=0.2cm] {right angle=L--O--M}; \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>>}}}] (K)--(L); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>>}}}] (N)--(M); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>}}}] (L)--(M); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>}}}] (K)--(N); % Vertex LABELS % Labels relative to shape geometry \node at ($(K)+(-0.2,-0.2)$) {K}; \node at ($(L)+(0.0,-0.2)$) {L}; \node at ($(O)+(0.2,-0.2)$) {O}; \node at ($(M)+(0.2,0.2)$) {M}; \node at ($(N)+(-0.2,0.2)$) {N}; % dotted/dashed arrows shifted away from edges % Horizontal side (A-B), shifted down yshift=0mm, \draw[<->, gray] ($(K) + (0,-0.7cm)$) -- ($(L) + (0,-0.7cm)$) node[black, midway, fill=white, inner sep=2.5pt] {9\,cm}; % Vertical side (D-C), shifted right xshift=0mm, \draw[<->, gray] ($(O)+(0.6,0)$) -- ($(O |- M)+(0.6,0)$) node[black, midway, fill=white, inner sep=2.5pt] {5\,cm}; \end{scope} \end{tikzpicture} \end{minipage}% \hfill \begin{minipage}{.4\textwidth} \begin{align*} \text{Area} &= \text{bh} \\ \text{Area} &= 9 \text{cm} \times 5 \text{cm} \\ \text{Area} &= 45 \text{cm}^2 \end{align*} \end{minipage} \par\vspace{1cm}\begin{minipage}{0.55\textwidth} \refstepcounter{minipagecount} \noindent{(\theminipagecount)}\quad \begin{tikzpicture}[scale=1.0, baseline=(current bounding box.north)] \begin{scope}[rotate=0] \coordinate (A) at (0,0); \coordinate (B) at (3.174,0); \coordinate (E) at ($(B)+(1.043,0)$); % extend out \coordinate (C) at ($(B)+(1.043,2.116)$); % Perpendicular upwards \coordinate (D) at ($(A)+(1.043,2.116)$); % Perpendicular upwards \draw (A)--(B)--(C)--(D)--cycle; \draw[dashed] (B)--(E); \draw[dashed] (E)--(C); \pic [draw, -, angle radius=0.2cm] {right angle=B--E--C}; \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>>}}}] (A)--(B); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>>}}}] (D)--(C); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>}}}] (B)--(C); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>}}}] (A)--(D); % Vertex LABELS % Labels relative to shape geometry \node at ($(A)+(-0.2,-0.2)$) {A}; \node at ($(B)+(0.0,-0.2)$) {B}; \node at ($(E)+(0.2,-0.2)$) {E}; \node at ($(C)+(0.2,0.2)$) {C}; \node at ($(D)+(-0.2,0.2)$) {D}; % dotted/dashed arrows shifted away from edges % Horizontal side (A-B), shifted down yshift=0mm, \draw[<->, gray] ($(A) + (0,-0.7cm)$) -- ($(B) + (0,-0.7cm)$) node[black, midway, fill=white, inner sep=2.5pt] {9\,cm}; % Vertical side (D-C), shifted right xshift=0mm, \draw[<->, gray] ($(E)+(0.6,0)$) -- ($(E |- C)+(0.6,0)$) node[black, midway, fill=white, inner sep=2.5pt] {6\,cm}; \end{scope} \end{tikzpicture} \end{minipage}% \hfill \begin{minipage}{.4\textwidth} \begin{align*} \text{Area} &= \text{bh} \\ \text{Area} &= 9 \text{cm} \times 6 \text{cm} \\ \text{Area} &= 54 \text{cm}^2 \end{align*} \end{minipage} \par\vspace{1cm}\begin{minipage}{0.55\textwidth} \refstepcounter{minipagecount} \noindent{(\theminipagecount)}\quad \begin{tikzpicture}[scale=1.0, baseline=(current bounding box.north)] \begin{scope}[rotate=0] \coordinate (V) at (0,0); \coordinate (W) at (3.232,0); \coordinate (Z) at ($(W)+(1.054,0)$); % extend out \coordinate (X) at ($(W)+(1.054,1.616)$); % Perpendicular upwards \coordinate (Y) at ($(V)+(1.054,1.616)$); % Perpendicular upwards \draw (V)--(W)--(X)--(Y)--cycle; \draw[dashed] (W)--(Z); \draw[dashed] (Z)--(X); \pic [draw, -, angle radius=0.2cm] {right angle=W--Z--X}; \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>>}}}] (V)--(W); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>>}}}] (Y)--(X); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>}}}] (W)--(X); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>}}}] (V)--(Y); % Vertex LABELS % Labels relative to shape geometry \node at ($(V)+(-0.2,-0.2)$) {V}; \node at ($(W)+(0.0,-0.2)$) {W}; \node at ($(Z)+(0.2,-0.2)$) {Z}; \node at ($(X)+(0.2,0.2)$) {X}; \node at ($(Y)+(-0.2,0.2)$) {Y}; % dotted/dashed arrows shifted away from edges % Horizontal side (A-B), shifted down yshift=0mm, \draw[<->, gray] ($(V) + (0,-0.7cm)$) -- ($(W) + (0,-0.7cm)$) node[black, midway, fill=white, inner sep=2.5pt] {6\,cm}; % Vertical side (D-C), shifted right xshift=0mm, \draw[<->, gray] ($(Z)+(0.6,0)$) -- ($(Z |- X)+(0.6,0)$) node[black, midway, fill=white, inner sep=2.5pt] {3\,cm}; \end{scope} \end{tikzpicture} \end{minipage}% \hfill \begin{minipage}{.4\textwidth} \begin{align*} \text{Area} &= \text{bh} \\ \text{Area} &= 6 \text{cm} \times 3 \text{cm} \\ \text{Area} &= 18 \text{cm}^2 \end{align*} \end{minipage} \par\vspace{1cm}\begin{minipage}{0.55\textwidth} \refstepcounter{minipagecount} \noindent{(\theminipagecount)}\quad \begin{tikzpicture}[scale=1.0, baseline=(current bounding box.north)] \begin{scope}[rotate=90] \coordinate (P) at (0,0); \coordinate (Q) at (5.164,0); \coordinate (T) at ($(Q)+(1.836,0)$); % extend out \coordinate (R) at ($(Q)+(1.836,1.721)$); % Perpendicular upwards \coordinate (S) at ($(P)+(1.836,1.721)$); % Perpendicular upwards \draw (P)--(Q)--(R)--(S)--cycle; \draw[dashed] (Q)--(T); \draw[dashed] (T)--(R); \pic [draw, -, angle radius=0.2cm] {right angle=Q--T--R}; \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>>}}}] (P)--(Q); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>>}}}] (S)--(R); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>}}}] (Q)--(R); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>}}}] (P)--(S); % Vertex LABELS % Labels relative to shape geometry \node at ($(P)+(-0.2,-0.2)$) {P}; \node at ($(Q)+(0.0,-0.2)$) {Q}; \node at ($(T)+(0.2,-0.2)$) {T}; \node at ($(R)+(0.2,0.2)$) {R}; \node at ($(S)+(-0.2,0.2)$) {S}; % dotted/dashed arrows shifted away from edges % Horizontal side (A-B), shifted down yshift=0mm, \draw[<->, gray] ($(P) + (0,-0.7cm)$) -- ($(Q) + (0,-0.7cm)$) node[black, midway, fill=white, inner sep=2.5pt] {9\,cm}; % Vertical side (D-C), shifted right xshift=0mm, \draw[<->, gray] ($(T)+(0.6,0)$) -- ($(T |- R)+(0.6,0)$) node[black, midway, fill=white, inner sep=2.5pt] {3\,cm}; \end{scope} \end{tikzpicture} \end{minipage}% \hfill \begin{minipage}{.4\textwidth} \begin{align*} \text{Area} &= \text{bh} \\ \text{Area} &= 9 \text{cm} \times 3 \text{cm} \\ \text{Area} &= 27 \text{cm}^2 \end{align*} \end{minipage} \par\vspace{1cm}\begin{minipage}{0.55\textwidth} \refstepcounter{minipagecount} \noindent{(\theminipagecount)}\quad \begin{tikzpicture}[scale=1.0, baseline=(current bounding box.north)] \begin{scope}[rotate=315] \coordinate (K) at (0,0); \coordinate (L) at (3.516,0); \coordinate (O) at ($(L)+(1.472,0)$); % extend out \coordinate (M) at ($(L)+(1.472,2.344)$); % Perpendicular upwards \coordinate (N) at ($(K)+(1.472,2.344)$); % Perpendicular upwards \draw (K)--(L)--(M)--(N)--cycle; \draw[dashed] (L)--(O); \draw[dashed] (O)--(M); \pic [draw, -, angle radius=0.2cm] {right angle=L--O--M}; \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>>}}}] (K)--(L); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>>}}}] (N)--(M); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>}}}] (L)--(M); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>}}}] (K)--(N); % Vertex LABELS % Labels relative to shape geometry \node at ($(K)+(-0.2,-0.2)$) {K}; \node at ($(L)+(0.0,-0.2)$) {L}; \node at ($(O)+(0.2,-0.2)$) {O}; \node at ($(M)+(0.2,0.2)$) {M}; \node at ($(N)+(-0.2,0.2)$) {N}; % dotted/dashed arrows shifted away from edges % Horizontal side (A-B), shifted down yshift=0mm, \draw[<->, gray] ($(K) + (0,-0.7cm)$) -- ($(L) + (0,-0.7cm)$) node[black, midway, fill=white, inner sep=2.5pt] {6\,cm}; % Vertical side (D-C), shifted right xshift=0mm, \draw[<->, gray] ($(O)+(0.6,0)$) -- ($(O |- M)+(0.6,0)$) node[black, midway, fill=white, inner sep=2.5pt] {4\,cm}; \end{scope} \end{tikzpicture} \end{minipage}% \hfill \begin{minipage}{.4\textwidth} \begin{align*} \text{Area} &= \text{bh} \\ \text{Area} &= 6 \text{cm} \times 4 \text{cm} \\ \text{Area} &= 24 \text{cm}^2 \end{align*} \end{minipage} \par\vspace{1cm}\begin{minipage}{0.55\textwidth} \refstepcounter{minipagecount} \noindent{(\theminipagecount)}\quad \begin{tikzpicture}[scale=1.0, baseline=(current bounding box.north)] \begin{scope}[rotate=270] \coordinate (V) at (0,0); \coordinate (W) at (3.94,0); \coordinate (Z) at ($(W)+(1.569,0)$); % extend out \coordinate (X) at ($(W)+(1.569,1.97)$); % Perpendicular upwards \coordinate (Y) at ($(V)+(1.569,1.97)$); % Perpendicular upwards \draw (V)--(W)--(X)--(Y)--cycle; \draw[dashed] (W)--(Z); \draw[dashed] (Z)--(X); \pic [draw, -, angle radius=0.2cm] {right angle=W--Z--X}; \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>>}}}] (V)--(W); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>>}}}] (Y)--(X); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>}}}] (W)--(X); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>}}}] (V)--(Y); % Vertex LABELS % Labels relative to shape geometry \node at ($(V)+(-0.2,-0.2)$) {V}; \node at ($(W)+(0.0,-0.2)$) {W}; \node at ($(Z)+(0.2,-0.2)$) {Z}; \node at ($(X)+(0.2,0.2)$) {X}; \node at ($(Y)+(-0.2,0.2)$) {Y}; % dotted/dashed arrows shifted away from edges % Horizontal side (A-B), shifted down yshift=0mm, \draw[<->, gray] ($(V) + (0,-0.7cm)$) -- ($(W) + (0,-0.7cm)$) node[black, midway, fill=white, inner sep=2.5pt] {8\,cm}; % Vertical side (D-C), shifted right xshift=0mm, \draw[<->, gray] ($(Z)+(0.6,0)$) -- ($(Z |- X)+(0.6,0)$) node[black, midway, fill=white, inner sep=2.5pt] {4\,cm}; \end{scope} \end{tikzpicture} \end{minipage}% \hfill \begin{minipage}{.4\textwidth} \begin{align*} \text{Area} &= \text{bh} \\ \text{Area} &= 8 \text{cm} \times 4 \text{cm} \\ \text{Area} &= 32 \text{cm}^2 \end{align*} \end{minipage} \par\vspace{1cm}\begin{minipage}{0.55\textwidth} \refstepcounter{minipagecount} \noindent{(\theminipagecount)}\quad \begin{tikzpicture}[scale=1.0, baseline=(current bounding box.north)] \begin{scope}[rotate=90] \coordinate (P) at (0,0); \coordinate (Q) at (2.882,0); \coordinate (T) at ($(Q)+(1.234,0)$); % extend out \coordinate (R) at ($(Q)+(1.234,2.47)$); % Perpendicular upwards \coordinate (S) at ($(P)+(1.234,2.47)$); % Perpendicular upwards \draw (P)--(Q)--(R)--(S)--cycle; \draw[dashed] (Q)--(T); \draw[dashed] (T)--(R); \pic [draw, -, angle radius=0.2cm] {right angle=Q--T--R}; \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>>}}}] (P)--(Q); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>>}}}] (S)--(R); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>}}}] (Q)--(R); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>}}}] (P)--(S); % Vertex LABELS % Labels relative to shape geometry \node at ($(P)+(-0.2,-0.2)$) {P}; \node at ($(Q)+(0.0,-0.2)$) {Q}; \node at ($(T)+(0.2,-0.2)$) {T}; \node at ($(R)+(0.2,0.2)$) {R}; \node at ($(S)+(-0.2,0.2)$) {S}; % dotted/dashed arrows shifted away from edges % Horizontal side (A-B), shifted down yshift=0mm, \draw[<->, gray] ($(P) + (0,-0.7cm)$) -- ($(Q) + (0,-0.7cm)$) node[black, midway, fill=white, inner sep=2.5pt] {7\,cm}; % Vertical side (D-C), shifted right xshift=0mm, \draw[<->, gray] ($(T)+(0.6,0)$) -- ($(T |- R)+(0.6,0)$) node[black, midway, fill=white, inner sep=2.5pt] {6\,cm}; \end{scope} \end{tikzpicture} \end{minipage}% \hfill \begin{minipage}{.4\textwidth} \begin{align*} \text{Area} &= \text{bh} \\ \text{Area} &= 7 \text{cm} \times 6 \text{cm} \\ \text{Area} &= 42 \text{cm}^2 \end{align*} \end{minipage} \par\vspace{1cm}\begin{minipage}{0.55\textwidth} \refstepcounter{minipagecount} \noindent{(\theminipagecount)}\quad \begin{tikzpicture}[scale=1.0, baseline=(current bounding box.north)] \begin{scope}[rotate=0] \coordinate (K) at (0,0); \coordinate (L) at (1.953,0); \coordinate (O) at ($(L)+(2.203,0)$); % extend out \coordinate (M) at ($(L)+(2.203,1.519)$); % Perpendicular upwards \coordinate (N) at ($(K)+(2.203,1.519)$); % Perpendicular upwards \draw (K)--(L)--(M)--(N)--cycle; \draw[dashed] (L)--(O); \draw[dashed] (O)--(M); \pic [draw, -, angle radius=0.2cm] {right angle=L--O--M}; \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>>}}}] (K)--(L); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>>}}}] (N)--(M); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>}}}] (L)--(M); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>}}}] (K)--(N); % Vertex LABELS % Labels relative to shape geometry \node at ($(K)+(-0.2,-0.2)$) {K}; \node at ($(L)+(0.0,-0.2)$) {L}; \node at ($(O)+(0.2,-0.2)$) {O}; \node at ($(M)+(0.2,0.2)$) {M}; \node at ($(N)+(-0.2,0.2)$) {N}; % dotted/dashed arrows shifted away from edges % Horizontal side (A-B), shifted down yshift=0mm, \draw[<->, gray] ($(K) + (0,-0.7cm)$) -- ($(L) + (0,-0.7cm)$) node[black, midway, fill=white, inner sep=2.5pt] {9\,cm}; % Vertical side (D-C), shifted right xshift=0mm, \draw[<->, gray] ($(O)+(0.6,0)$) -- ($(O |- M)+(0.6,0)$) node[black, midway, fill=white, inner sep=2.5pt] {7\,cm}; \end{scope} \end{tikzpicture} \end{minipage}% \hfill \begin{minipage}{.4\textwidth} \begin{align*} \text{Area} &= \text{bh} \\ \text{Area} &= 9 \text{cm} \times 7 \text{cm} \\ \text{Area} &= 63 \text{cm}^2 \end{align*} \end{minipage} \par\vspace{1cm}\begin{minipage}{0.55\textwidth} \refstepcounter{minipagecount} \noindent{(\theminipagecount)}\quad \begin{tikzpicture}[scale=1.0, baseline=(current bounding box.north)] \begin{scope}[rotate=225] \coordinate (V) at (0,0); \coordinate (W) at (4.747,0); \coordinate (Z) at ($(W)+(1.986,0)$); % extend out \coordinate (X) at ($(W)+(1.986,1.78)$); % Perpendicular upwards \coordinate (Y) at ($(V)+(1.986,1.78)$); % Perpendicular upwards \draw (V)--(W)--(X)--(Y)--cycle; \draw[dashed] (W)--(Z); \draw[dashed] (Z)--(X); \pic [draw, -, angle radius=0.2cm] {right angle=W--Z--X}; \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>>}}}] (V)--(W); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>>}}}] (Y)--(X); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>}}}] (W)--(X); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>}}}] (V)--(Y); % Vertex LABELS % Labels relative to shape geometry \node at ($(V)+(-0.2,-0.2)$) {V}; \node at ($(W)+(0.0,-0.2)$) {W}; \node at ($(Z)+(0.2,-0.2)$) {Z}; \node at ($(X)+(0.2,0.2)$) {X}; \node at ($(Y)+(-0.2,0.2)$) {Y}; % dotted/dashed arrows shifted away from edges % Horizontal side (A-B), shifted down yshift=0mm, \draw[<->, gray] ($(V) + (0,-0.7cm)$) -- ($(W) + (0,-0.7cm)$) node[black, midway, fill=white, inner sep=2.5pt] {8\,cm}; % Vertical side (D-C), shifted right xshift=0mm, \draw[<->, gray] ($(Z)+(0.6,0)$) -- ($(Z |- X)+(0.6,0)$) node[black, midway, fill=white, inner sep=2.5pt] {3\,cm}; \end{scope} \end{tikzpicture} \end{minipage}% \hfill \begin{minipage}{.4\textwidth} \begin{align*} \text{Area} &= \text{bh} \\ \text{Area} &= 8 \text{cm} \times 3 \text{cm} \\ \text{Area} &= 24 \text{cm}^2 \end{align*} \end{minipage} \par\vspace{1cm}\begin{minipage}{0.55\textwidth} \refstepcounter{minipagecount} \noindent{(\theminipagecount)}\quad \begin{tikzpicture}[scale=1.0, baseline=(current bounding box.north)] \begin{scope}[rotate=170] \coordinate (P) at (0,0); \coordinate (Q) at (5.366,0); \coordinate (T) at ($(Q)+(1.634,0)$); % extend out \coordinate (R) at ($(Q)+(1.634,1.789)$); % Perpendicular upwards \coordinate (S) at ($(P)+(1.634,1.789)$); % Perpendicular upwards \draw (P)--(Q)--(R)--(S)--cycle; \draw[dashed] (Q)--(T); \draw[dashed] (T)--(R); \pic [draw, -, angle radius=0.2cm] {right angle=Q--T--R}; \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>>}}}] (P)--(Q); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>>}}}] (S)--(R); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>}}}] (Q)--(R); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>}}}] (P)--(S); % Vertex LABELS % Labels relative to shape geometry \node at ($(P)+(-0.2,-0.2)$) {P}; \node at ($(Q)+(0.0,-0.2)$) {Q}; \node at ($(T)+(0.2,-0.2)$) {T}; \node at ($(R)+(0.2,0.2)$) {R}; \node at ($(S)+(-0.2,0.2)$) {S}; % dotted/dashed arrows shifted away from edges % Horizontal side (A-B), shifted down yshift=0mm, \draw[<->, gray] ($(P) + (0,-0.7cm)$) -- ($(Q) + (0,-0.7cm)$) node[black, midway, fill=white, inner sep=2.5pt] {6\,cm}; % Vertical side (D-C), shifted right xshift=0mm, \draw[<->, gray] ($(T)+(0.6,0)$) -- ($(T |- R)+(0.6,0)$) node[black, midway, fill=white, inner sep=2.5pt] {2\,cm}; \end{scope} \end{tikzpicture} \end{minipage}% \hfill \begin{minipage}{.4\textwidth} \begin{align*} \text{Area} &= \text{bh} \\ \text{Area} &= 6 \text{cm} \times 2 \text{cm} \\ \text{Area} &= 12 \text{cm}^2 \end{align*} \end{minipage} \par\vspace{1cm}\begin{minipage}{0.55\textwidth} \refstepcounter{minipagecount} \noindent{(\theminipagecount)}\quad \begin{tikzpicture}[scale=1.0, baseline=(current bounding box.north)] \begin{scope}[rotate=0] \coordinate (P) at (0,0); \coordinate (Q) at (2.45,0); \coordinate (T) at ($(Q)+(2.166,0)$); % extend out \coordinate (R) at ($(Q)+(2.166,1.96)$); % Perpendicular upwards \coordinate (S) at ($(P)+(2.166,1.96)$); % Perpendicular upwards \draw (P)--(Q)--(R)--(S)--cycle; \draw[dashed] (Q)--(T); \draw[dashed] (T)--(R); \pic [draw, -, angle radius=0.2cm] {right angle=Q--T--R}; \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>>}}}] (P)--(Q); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>>}}}] (S)--(R); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>}}}] (Q)--(R); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>}}}] (P)--(S); % Vertex LABELS % Labels relative to shape geometry \node at ($(P)+(-0.2,-0.2)$) {P}; \node at ($(Q)+(0.0,-0.2)$) {Q}; \node at ($(T)+(0.2,-0.2)$) {T}; \node at ($(R)+(0.2,0.2)$) {R}; \node at ($(S)+(-0.2,0.2)$) {S}; % dotted/dashed arrows shifted away from edges % Horizontal side (A-B), shifted down yshift=0mm, \draw[<->, gray] ($(P) + (0,-0.7cm)$) -- ($(Q) + (0,-0.7cm)$) node[black, midway, fill=white, inner sep=2.5pt] {5\,cm}; % Vertical side (D-C), shifted right xshift=0mm, \draw[<->, gray] ($(T)+(0.6,0)$) -- ($(T |- R)+(0.6,0)$) node[black, midway, fill=white, inner sep=2.5pt] {4\,cm}; \end{scope} \end{tikzpicture} \end{minipage}% \hfill \begin{minipage}{.4\textwidth} \begin{align*} \text{Area} &= \text{bh} \\ \text{Area} &= 5 \text{cm} \times 4 \text{cm} \\ \text{Area} &= 20 \text{cm}^2 \end{align*} \end{minipage} \par\vspace{1cm}\begin{minipage}{0.55\textwidth} \refstepcounter{minipagecount} \noindent{(\theminipagecount)}\quad \begin{tikzpicture}[scale=1.0, baseline=(current bounding box.north)] \begin{scope}[rotate=0] \coordinate (F) at (0,0); \coordinate (G) at (2.989,0); \coordinate (J) at ($(G)+(2.288,0)$); % extend out \coordinate (H) at ($(G)+(2.288,2.242)$); % Perpendicular upwards \coordinate (I) at ($(F)+(2.288,2.242)$); % Perpendicular upwards \draw (F)--(G)--(H)--(I)--cycle; \draw[dashed] (G)--(J); \draw[dashed] (J)--(H); \pic [draw, -, angle radius=0.2cm] {right angle=G--J--H}; \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>>}}}] (F)--(G); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>>}}}] (I)--(H); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>}}}] (G)--(H); \draw[>=Straight Barb, postaction={decorate}, decoration={markings, mark=at position 0.5 with {\arrow[scale=1.5]{>}}}] (F)--(I); % Vertex LABELS % Labels relative to shape geometry \node at ($(F)+(-0.2,-0.2)$) {F}; \node at ($(G)+(0.0,-0.2)$) {G}; \node at ($(J)+(0.2,-0.2)$) {J}; \node at ($(H)+(0.2,0.2)$) {H}; \node at ($(I)+(-0.2,0.2)$) {I}; % dotted/dashed arrows shifted away from edges % Horizontal side (A-B), shifted down yshift=0mm, \draw[<->, gray] ($(F) + (0,-0.7cm)$) -- ($(G) + (0,-0.7cm)$) node[black, midway, fill=white, inner sep=2.5pt] {8\,cm}; % Vertical side (D-C), shifted right xshift=0mm, \draw[<->, gray] ($(J)+(0.6,0)$) -- ($(J |- H)+(0.6,0)$) node[black, midway, fill=white, inner sep=2.5pt] {6\,cm}; \end{scope} \end{tikzpicture} \end{minipage}% \hfill \begin{minipage}{.4\textwidth} \begin{align*} \text{Area} &= \text{bh} \\ \text{Area} &= 8 \text{cm} \times 6 \text{cm} \\ \text{Area} &= 48 \text{cm}^2 \end{align*} \end{minipage} \par\vspace{1cm} \end{document}