\documentclass[12pt]{article} \usepackage{tikz} \usepackage{amsmath} % Underlining package \usepackage{ulem} \usetikzlibrary{calc} \usetikzlibrary{angles,quotes} \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 (E) at (0,0); \coordinate (F) at (2.447,0); \coordinate (H) at ($(F)+(1.379,0)$); % extend out \coordinate (G) at ($(H)+(0,1.835)$); % Perpendicular upwards \draw (E)--(F)--(G)--cycle; \draw[dashed] (F)--(H); \draw[dashed] (H)--(G); \pic [draw, -, angle radius=0.2cm] {right angle=G--H--F}; % Vertex LABELS % Labels relative to shape geometry \node at ($(E)+(-0.2,-0.2)$) {E}; \node at ($(F)+(0.0,-0.2)$) {F}; \node at ($(H)+(0.2,-0.2)$) {H}; \node at ($(G)+(0.2,0.2)$) {G}; % dotted/dashed arrows shifted away from edges % Horizontal side (A-B), shifted down yshift=0mm, \draw[<->, gray] ($(E) + (0,-0.7cm)$) -- ($(F) + (0,-0.7cm)$) node[black, midway, fill=white, inner sep=2.5pt] {4\,cm}; % Vertical side (D-C), shifted right xshift=0mm, \draw[<->, gray] ($(H)+(0.6,0)$) -- ($(H |- G)+(0.6,0)$) 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} &= \frac{1}{2} \text{bh} \\ \text{Area} &= \frac{1}{2} \times 4 \text{cm} \times 3 \text{cm} \\ \text{Area} &= 6.0 \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=190] \coordinate (E) at (0,0); \coordinate (F) at (3.6,0); \coordinate (H) at (0.955,0); \coordinate (G) at ($(H)+(0,2.057)$); % Perpendicular upwards \draw (E)--(F)--(G)--cycle; \draw[dashed] (H)--(G); \pic [draw, -, angle radius=0.2cm] {right angle=G--H--F}; % Vertex LABELS % Labels relative to shape geometry \node at ($(E)+(-0.2,-0.2)$) {E}; \node at ($(F)+(0.2,-0.2)$) {F}; \node at ($(H)+(0.0,-0.2)$) {H}; \node at ($(G)+(0.2,0.2)$) {G}; % dotted/dashed arrows shifted away from edges % Horizontal side (A-B), shifted down ift=0mm, \draw[<->, gray] ($(E) + (0,-1.0cm)$) -- ($(F) + (0,-1.0cm)$) node[black, midway, fill=white, inner sep=2.5pt] {7\,cm}; % Vertical side (B-C), shifted right xshift=0mm, \draw[<->, gray] ($(F |- H)+(0.6,0)$) -- ($(F |- G)+(0.6,0)$) 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} &= \frac{1}{2} \text{bh} \\ \text{Area} &= \frac{1}{2} \times 7 \text{cm} \times 4 \text{cm} \\ \text{Area} &= 14.0 \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 (K) at (0,0); \coordinate (L) at (4.132,0); \coordinate (N) at (1.325,0); \coordinate (M) at ($(N)+(0,1.771)$); % Perpendicular upwards \draw (K)--(L)--(M)--cycle; \draw[dashed] (N)--(M); \pic [draw, -, angle radius=0.2cm] {right angle=M--N--L}; % Vertex LABELS % Labels relative to shape geometry \node at ($(K)+(-0.2,-0.2)$) {K}; \node at ($(L)+(0.2,-0.2)$) {L}; \node at ($(N)+(0.0,-0.2)$) {N}; \node at ($(M)+(0.2,0.2)$) {M}; % dotted/dashed arrows shifted away from edges % Horizontal side (A-B), shifted down ift=0mm, \draw[<->, gray] ($(K) + (0,-1.0cm)$) -- ($(L) + (0,-1.0cm)$) node[black, midway, fill=white, inner sep=2.5pt] {7\,cm}; % Vertical side (B-C), shifted right xshift=0mm, \draw[<->, gray] ($(L |- N)+(0.6,0)$) -- ($(L |- M)+(0.6,0)$) 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} &= \frac{1}{2} \text{bh} \\ \text{Area} &= \frac{1}{2} \times 7 \text{cm} \times 3 \text{cm} \\ \text{Area} &= 10.5 \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] % Draw \draw (0,0) coordinate (E) -- ++(1.945,0) coordinate (F) -- ++(90:1.621) coordinate (G) -- cycle; \pic [draw, -, angle radius=0.2cm] {right angle=G--F--E}; % Vertex LABELS % Labels relative to shape geometry \node at ($(E)+(-0.2,-0.2)$) {E}; \node at ($(F)+(0.2,-0.2)$) {F}; \node at ($(G)+(0.2,0.2)$) {G}; % dotted/dashed arrows shifted away from edges % Horizontal side (A-B), shifted down \draw[<->, gray] ($(E) + (0,-0.6cm)$) -- ($(F) + (0,-0.6cm)$) node[black, midway, fill=white, inner sep=2.5pt] {6\,cm}; % Vertical side (B-C), shifted right \draw[<->, gray] ($(F) + (0.6cm,0)$) -- ($(G) + (0.6cm,0)$) node[black, midway, fill=white, xshift=0mm, inner sep=2.5pt] {5\,cm}; \end{scope} \end{tikzpicture} \end{minipage}% \hfill \begin{minipage}{.4\textwidth} \begin{align*} \text{Area} &= \frac{1}{2} \text{bh} \\ \text{Area} &= \frac{1}{2} \times 6 \text{cm} \times 5 \text{cm} \\ \text{Area} &= 15.0 \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 (A) at (0,0); \coordinate (B) at (3.131,0); \coordinate (D) at (2.271,0); \coordinate (C) at ($(D)+(0,2.087)$); % Perpendicular upwards \draw (A)--(B)--(C)--cycle; \draw[dashed] (D)--(C); \pic [draw, -, angle radius=0.2cm] {right angle=C--D--B}; % Vertex LABELS % Labels relative to shape geometry \node at ($(A)+(-0.2,-0.2)$) {A}; \node at ($(B)+(0.2,-0.2)$) {B}; \node at ($(D)+(0.0,-0.2)$) {D}; \node at ($(C)+(0.2,0.2)$) {C}; % dotted/dashed arrows shifted away from edges % Horizontal side (A-B), shifted down ift=0mm, \draw[<->, gray] ($(A) + (0,-1.0cm)$) -- ($(B) + (0,-1.0cm)$) node[black, midway, fill=white, inner sep=2.5pt] {6\,cm}; % Vertical side (B-C), shifted right xshift=0mm, \draw[<->, gray] ($(B |- D)+(0.6,0)$) -- ($(B |- C)+(0.6,0)$) 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} &= \frac{1}{2} \text{bh} \\ \text{Area} &= \frac{1}{2} \times 6 \text{cm} \times 4 \text{cm} \\ \text{Area} &= 12.0 \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 (W) at (0,0); \coordinate (X) at (2.817,0); \coordinate (Z) at (0.518,0); \coordinate (Y) at ($(Z)+(0,1.878)$); % Perpendicular upwards \draw (W)--(X)--(Y)--cycle; \draw[dashed] (Z)--(Y); \pic [draw, -, angle radius=0.2cm] {right angle=Y--Z--X}; % Vertex LABELS % Labels relative to shape geometry \node at ($(W)+(-0.2,-0.2)$) {W}; \node at ($(X)+(0.2,-0.2)$) {X}; \node at ($(Z)+(0.0,-0.2)$) {Z}; \node at ($(Y)+(0.2,0.2)$) {Y}; % dotted/dashed arrows shifted away from edges % Horizontal side (A-B), shifted down ift=0mm, \draw[<->, gray] ($(W) + (0,-1.0cm)$) -- ($(X) + (0,-1.0cm)$) node[black, midway, fill=white, inner sep=2.5pt] {3\,cm}; % Vertical side (B-C), shifted right xshift=0mm, \draw[<->, gray] ($(X |- Z)+(0.6,0)$) -- ($(X |- Y)+(0.6,0)$) 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} &= \frac{1}{2} \text{bh} \\ \text{Area} &= \frac{1}{2} \times 3 \text{cm} \times 2 \text{cm} \\ \text{Area} &= 3.0 \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 (4.995,0); \coordinate (N) at ($(L)+(1.005,0)$); % extend out \coordinate (M) at ($(N)+(0,1.873)$); % Perpendicular upwards \draw (K)--(L)--(M)--cycle; \draw[dashed] (L)--(N); \draw[dashed] (N)--(M); \pic [draw, -, angle radius=0.2cm] {right angle=M--N--L}; % 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 ($(N)+(0.2,-0.2)$) {N}; \node at ($(M)+(0.2,0.2)$) {M}; % 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] ($(N)+(0.6,0)$) -- ($(N |- M)+(0.6,0)$) 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} &= \frac{1}{2} \text{bh} \\ \text{Area} &= \frac{1}{2} \times 8 \text{cm} \times 3 \text{cm} \\ \text{Area} &= 12.0 \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] % Draw \draw (0,0) coordinate (E) -- ++(3.321,0) coordinate (F) -- ++(90:2.372) coordinate (G) -- cycle; \pic [draw, -, angle radius=0.2cm] {right angle=G--F--E}; % Vertex LABELS % Labels relative to shape geometry \node at ($(E)+(-0.2,-0.2)$) {E}; \node at ($(F)+(0.2,-0.2)$) {F}; \node at ($(G)+(0.2,0.2)$) {G}; % dotted/dashed arrows shifted away from edges % Horizontal side (A-B), shifted down \draw[<->, gray] ($(E) + (0,-0.6cm)$) -- ($(F) + (0,-0.6cm)$) node[black, midway, fill=white, inner sep=2.5pt] {7\,cm}; % Vertical side (B-C), shifted right \draw[<->, gray] ($(F) + (0.6cm,0)$) -- ($(G) + (0.6cm,0)$) node[black, midway, fill=white, xshift=0mm, inner sep=2.5pt] {5\,cm}; \end{scope} \end{tikzpicture} \end{minipage}% \hfill \begin{minipage}{.4\textwidth} \begin{align*} \text{Area} &= \frac{1}{2} \text{bh} \\ \text{Area} &= \frac{1}{2} \times 7 \text{cm} \times 5 \text{cm} \\ \text{Area} &= 17.5 \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] % Draw \draw (0,0) coordinate (R) -- ++(5.589,0) coordinate (S) -- ++(90:2.484) coordinate (T) -- cycle; \pic [draw, -, angle radius=0.2cm] {right angle=T--S--R}; % Vertex LABELS % Labels relative to shape geometry \node at ($(R)+(-0.2,-0.2)$) {R}; \node at ($(S)+(0.2,-0.2)$) {S}; \node at ($(T)+(0.2,0.2)$) {T}; % dotted/dashed arrows shifted away from edges % Horizontal side (A-B), shifted down \draw[<->, gray] ($(R) + (0,-0.6cm)$) -- ($(S) + (0,-0.6cm)$) node[black, midway, fill=white, inner sep=2.5pt] {9\,cm}; % Vertical side (B-C), shifted right \draw[<->, gray] ($(S) + (0.6cm,0)$) -- ($(T) + (0.6cm,0)$) node[black, midway, fill=white, xshift=0mm, inner sep=2.5pt] {4\,cm}; \end{scope} \end{tikzpicture} \end{minipage}% \hfill \begin{minipage}{.4\textwidth} \begin{align*} \text{Area} &= \frac{1}{2} \text{bh} \\ \text{Area} &= \frac{1}{2} \times 9 \text{cm} \times 4 \text{cm} \\ \text{Area} &= 18.0 \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 (4.197,0); \coordinate (D) at (0.635,0); \coordinate (C) at ($(D)+(0,1.679)$); % Perpendicular upwards \draw (A)--(B)--(C)--cycle; \draw[dashed] (D)--(C); \pic [draw, -, angle radius=0.2cm] {right angle=C--D--B}; % Vertex LABELS % Labels relative to shape geometry \node at ($(A)+(-0.2,-0.2)$) {A}; \node at ($(B)+(0.2,-0.2)$) {B}; \node at ($(D)+(0.0,-0.2)$) {D}; \node at ($(C)+(0.2,0.2)$) {C}; % dotted/dashed arrows shifted away from edges % Horizontal side (A-B), shifted down ift=0mm, \draw[<->, gray] ($(A) + (0,-1.0cm)$) -- ($(B) + (0,-1.0cm)$) node[black, midway, fill=white, inner sep=2.5pt] {5\,cm}; % Vertical side (B-C), shifted right xshift=0mm, \draw[<->, gray] ($(B |- D)+(0.6,0)$) -- ($(B |- C)+(0.6,0)$) 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} &= \frac{1}{2} \text{bh} \\ \text{Area} &= \frac{1}{2} \times 5 \text{cm} \times 2 \text{cm} \\ \text{Area} &= 5.0 \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 (W) at (0,0); \coordinate (X) at (6.0,0); \coordinate (Z) at (3.422,0); \coordinate (Y) at ($(Z)+(0,1.714)$); % Perpendicular upwards \draw (W)--(X)--(Y)--cycle; \draw[dashed] (Z)--(Y); \pic [draw, -, angle radius=0.2cm] {right angle=Y--Z--X}; % Vertex LABELS % Labels relative to shape geometry \node at ($(W)+(-0.2,-0.2)$) {W}; \node at ($(X)+(0.2,-0.2)$) {X}; \node at ($(Z)+(0.0,-0.2)$) {Z}; \node at ($(Y)+(0.2,0.2)$) {Y}; % dotted/dashed arrows shifted away from edges % Horizontal side (A-B), shifted down ift=0mm, \draw[<->, gray] ($(W) + (0,-1.0cm)$) -- ($(X) + (0,-1.0cm)$) node[black, midway, fill=white, inner sep=2.5pt] {7\,cm}; % Vertical side (B-C), shifted right xshift=0mm, \draw[<->, gray] ($(X |- Z)+(0.6,0)$) -- ($(X |- Y)+(0.6,0)$) 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} &= \frac{1}{2} \text{bh} \\ \text{Area} &= \frac{1}{2} \times 7 \text{cm} \times 2 \text{cm} \\ \text{Area} &= 7.0 \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=80] % Draw \draw (0,0) coordinate (E) -- ++(3.046,0) coordinate (F) -- ++(90:1.523) coordinate (G) -- cycle; \pic [draw, -, angle radius=0.2cm] {right angle=G--F--E}; % Vertex LABELS % Labels relative to shape geometry \node at ($(E)+(-0.2,-0.2)$) {E}; \node at ($(F)+(0.2,-0.2)$) {F}; \node at ($(G)+(0.2,0.2)$) {G}; % dotted/dashed arrows shifted away from edges % Horizontal side (A-B), shifted down \draw[<->, gray] ($(E) + (0,-0.6cm)$) -- ($(F) + (0,-0.6cm)$) node[black, midway, fill=white, inner sep=2.5pt] {8\,cm}; % Vertical side (B-C), shifted right \draw[<->, gray] ($(F) + (0.6cm,0)$) -- ($(G) + (0.6cm,0)$) node[black, midway, fill=white, xshift=0mm, inner sep=2.5pt] {4\,cm}; \end{scope} \end{tikzpicture} \end{minipage}% \hfill \begin{minipage}{.4\textwidth} \begin{align*} \text{Area} &= \frac{1}{2} \text{bh} \\ \text{Area} &= \frac{1}{2} \times 8 \text{cm} \times 4 \text{cm} \\ \text{Area} &= 16.0 \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 (A) at (0,0); \coordinate (B) at (3.967,0); \coordinate (D) at ($(B)+(0.728,0)$); % extend out \coordinate (C) at ($(D)+(0,2.38)$); % Perpendicular upwards \draw (A)--(B)--(C)--cycle; \draw[dashed] (B)--(D); \draw[dashed] (D)--(C); \pic [draw, -, angle radius=0.2cm] {right angle=C--D--B}; % 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 ($(D)+(0.2,-0.2)$) {D}; \node at ($(C)+(0.2,0.2)$) {C}; % 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] {5\,cm}; % Vertical side (D-C), shifted right xshift=0mm, \draw[<->, gray] ($(D)+(0.6,0)$) -- ($(D |- C)+(0.6,0)$) 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} &= \frac{1}{2} \text{bh} \\ \text{Area} &= \frac{1}{2} \times 5 \text{cm} \times 3 \text{cm} \\ \text{Area} &= 7.5 \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 (K) at (0,0); \coordinate (L) at (5.928,0); \coordinate (N) at (4.631,0); \coordinate (M) at ($(N)+(0,1.976)$); % Perpendicular upwards \draw (K)--(L)--(M)--cycle; \draw[dashed] (N)--(M); \pic [draw, -, angle radius=0.2cm] {right angle=M--N--L}; % Vertex LABELS % Labels relative to shape geometry \node at ($(K)+(-0.2,-0.2)$) {K}; \node at ($(L)+(0.2,-0.2)$) {L}; \node at ($(N)+(0.0,-0.2)$) {N}; \node at ($(M)+(0.2,0.2)$) {M}; % dotted/dashed arrows shifted away from edges % Horizontal side (A-B), shifted down ift=0mm, \draw[<->, gray] ($(K) + (0,-1.0cm)$) -- ($(L) + (0,-1.0cm)$) node[black, midway, fill=white, inner sep=2.5pt] {6\,cm}; % Vertical side (B-C), shifted right xshift=0mm, \draw[<->, gray] ($(L |- N)+(0.6,0)$) -- ($(L |- M)+(0.6,0)$) 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} &= \frac{1}{2} \text{bh} \\ \text{Area} &= \frac{1}{2} \times 6 \text{cm} \times 2 \text{cm} \\ \text{Area} &= 6.0 \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] % Draw \draw (0,0) coordinate (R) -- ++(6.0,0) coordinate (S) -- ++(90:2.0) coordinate (T) -- cycle; \pic [draw, -, angle radius=0.2cm] {right angle=T--S--R}; % Vertex LABELS % Labels relative to shape geometry \node at ($(R)+(-0.2,-0.2)$) {R}; \node at ($(S)+(0.2,-0.2)$) {S}; \node at ($(T)+(0.2,0.2)$) {T}; % dotted/dashed arrows shifted away from edges % Horizontal side (A-B), shifted down \draw[<->, gray] ($(R) + (0,-0.6cm)$) -- ($(S) + (0,-0.6cm)$) node[black, midway, fill=white, inner sep=2.5pt] {9\,cm}; % Vertical side (B-C), shifted right \draw[<->, gray] ($(S) + (0.6cm,0)$) -- ($(T) + (0.6cm,0)$) node[black, midway, fill=white, xshift=0mm, inner sep=2.5pt] {3\,cm}; \end{scope} \end{tikzpicture} \end{minipage}% \hfill \begin{minipage}{.4\textwidth} \begin{align*} \text{Area} &= \frac{1}{2} \text{bh} \\ \text{Area} &= \frac{1}{2} \times 9 \text{cm} \times 3 \text{cm} \\ \text{Area} &= 13.5 \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] % Draw \draw (0,0) coordinate (E) -- ++(2.711,0) coordinate (F) -- ++(90:2.169) coordinate (G) -- cycle; \pic [draw, -, angle radius=0.2cm] {right angle=G--F--E}; % Vertex LABELS % Labels relative to shape geometry \node at ($(E)+(-0.2,-0.2)$) {E}; \node at ($(F)+(0.2,-0.2)$) {F}; \node at ($(G)+(0.2,0.2)$) {G}; % dotted/dashed arrows shifted away from edges % Horizontal side (A-B), shifted down \draw[<->, gray] ($(E) + (0,-0.6cm)$) -- ($(F) + (0,-0.6cm)$) node[black, midway, fill=white, inner sep=2.5pt] {5\,cm}; % Vertical side (B-C), shifted right \draw[<->, gray] ($(F) + (0.6cm,0)$) -- ($(G) + (0.6cm,0)$) node[black, midway, fill=white, xshift=0mm, inner sep=2.5pt] {4\,cm}; \end{scope} \end{tikzpicture} \end{minipage}% \hfill \begin{minipage}{.4\textwidth} \begin{align*} \text{Area} &= \frac{1}{2} \text{bh} \\ \text{Area} &= \frac{1}{2} \times 5 \text{cm} \times 4 \text{cm} \\ \text{Area} &= 10.0 \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 (Q) at (0,0); \coordinate (R) at (2.881,0); \coordinate (T) at ($(R)+(1.494,0)$); % extend out \coordinate (S) at ($(T)+(0,2.161)$); % Perpendicular upwards \draw (Q)--(R)--(S)--cycle; \draw[dashed] (R)--(T); \draw[dashed] (T)--(S); \pic [draw, -, angle radius=0.2cm] {right angle=S--T--R}; % Vertex LABELS % Labels relative to shape geometry \node at ($(Q)+(-0.2,-0.2)$) {Q}; \node at ($(R)+(0.0,-0.2)$) {R}; \node at ($(T)+(0.2,-0.2)$) {T}; \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] ($(Q) + (0,-0.7cm)$) -- ($(R) + (0,-0.7cm)$) node[black, midway, fill=white, inner sep=2.5pt] {8\,cm}; % Vertical side (D-C), shifted right xshift=0mm, \draw[<->, gray] ($(T)+(0.6,0)$) -- ($(T |- S)+(0.6,0)$) 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} &= \frac{1}{2} \text{bh} \\ \text{Area} &= \frac{1}{2} \times 8 \text{cm} \times 6 \text{cm} \\ \text{Area} &= 24.0 \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 (K) at (0,0); \coordinate (L) at (2.229,0); \coordinate (N) at ($(L)+(1.47,0)$); % extend out \coordinate (M) at ($(N)+(0,1.95)$); % Perpendicular upwards \draw (K)--(L)--(M)--cycle; \draw[dashed] (L)--(N); \draw[dashed] (N)--(M); \pic [draw, -, angle radius=0.2cm] {right angle=M--N--L}; % 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 ($(N)+(0.2,-0.2)$) {N}; \node at ($(M)+(0.2,0.2)$) {M}; % 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] ($(N)+(0.6,0)$) -- ($(N |- M)+(0.6,0)$) 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} &= \frac{1}{2} \text{bh} \\ \text{Area} &= \frac{1}{2} \times 8 \text{cm} \times 7 \text{cm} \\ \text{Area} &= 28.0 \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 (E) at (0,0); \coordinate (F) at (3.992,0); \coordinate (H) at (0.604,0); \coordinate (G) at ($(H)+(0,2.495)$); % Perpendicular upwards \draw (E)--(F)--(G)--cycle; \draw[dashed] (H)--(G); \pic [draw, -, angle radius=0.2cm] {right angle=G--H--F}; % Vertex LABELS % Labels relative to shape geometry \node at ($(E)+(-0.2,-0.2)$) {E}; \node at ($(F)+(0.2,-0.2)$) {F}; \node at ($(H)+(0.0,-0.2)$) {H}; \node at ($(G)+(0.2,0.2)$) {G}; % dotted/dashed arrows shifted away from edges % Horizontal side (A-B), shifted down ift=0mm, \draw[<->, gray] ($(E) + (0,-1.0cm)$) -- ($(F) + (0,-1.0cm)$) node[black, midway, fill=white, inner sep=2.5pt] {8\,cm}; % Vertical side (B-C), shifted right xshift=0mm, \draw[<->, gray] ($(F |- H)+(0.6,0)$) -- ($(F |- G)+(0.6,0)$) 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} &= \frac{1}{2} \text{bh} \\ \text{Area} &= \frac{1}{2} \times 8 \text{cm} \times 5 \text{cm} \\ \text{Area} &= 20.0 \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] % Draw \draw (0,0) coordinate (K) -- ++(4.552,0) coordinate (L) -- ++(90:2.276) coordinate (M) -- cycle; \pic [draw, -, angle radius=0.2cm] {right angle=M--L--K}; % Vertex LABELS % Labels relative to shape geometry \node at ($(K)+(-0.2,-0.2)$) {K}; \node at ($(L)+(0.2,-0.2)$) {L}; \node at ($(M)+(0.2,0.2)$) {M}; % dotted/dashed arrows shifted away from edges % Horizontal side (A-B), shifted down \draw[<->, gray] ($(K) + (0,-0.6cm)$) -- ($(L) + (0,-0.6cm)$) node[black, midway, fill=white, inner sep=2.5pt] {4\,cm}; % Vertical side (B-C), shifted right \draw[<->, gray] ($(L) + (0.6cm,0)$) -- ($(M) + (0.6cm,0)$) node[black, midway, fill=white, xshift=0mm, inner sep=2.5pt] {2\,cm}; \end{scope} \end{tikzpicture} \end{minipage}% \hfill \begin{minipage}{.4\textwidth} \begin{align*} \text{Area} &= \frac{1}{2} \text{bh} \\ \text{Area} &= \frac{1}{2} \times 4 \text{cm} \times 2 \text{cm} \\ \text{Area} &= 4.0 \text{cm}^2 \end{align*} \end{minipage} \par\vspace{1cm} \end{document}