Resources for Area of Kites and Rhombuses
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Area of Kites and Rhombuses Theory
![\begin{tabular}{p{11cm}c} \begin{tabular}{p{10cm}} The area of a kite is half the product of its diagonals.\newline Let \(A C=x\) and \(DB=y\)\newline \begin{tabular}{c} \(\therefore \text { Area }=\dfrac{1}{2}xy\) \end{tabular} \end{tabular} & \begin{tabular}{c} \begin{tikzpicture}[scale=0.9] \coordinate[label=left:D] (O) at (0,0); \coordinate[label=above:A] (A) at (45:2cm); \coordinate[label=below:C] (B) at (-45:2cm); \coordinate[label=right:B] (C) at (right:5cm); \coordinate (D) at ($(O)!(A)!(C)$); \draw[line width=1pt] (O)--(A)node[midway,rotate=-45]{\Large -}--(C)node[midway,rotate=45]{=} --(B)node[midway,rotate=-45]{=}--(O)node[midway,rotate=45]{\Large -}; \draw[line width=1pt,densely dashed] (A)--(B); \draw[line width=1pt,densely dashed] (O)--(C); \pic [draw=black,line width=1pt,angle radius=0.4cm,angle eccentricity=1.6,""] {right angle=A--D--C}; \end{tikzpicture} \end{tabular} \end{tabular} \begin{tabular}{p{11cm}c} \begin{tabular}{p{11cm}} The area of a rhombus is half the product of its diagonals.\newline Let \(AC=x\) and \(DB=y\)\newline \(\therefore \text { Area }=\dfrac{1}{2} x y\) \end{tabular} & \begin{tabular}{c} \begin{tikzpicture}[scale=1] \coordinate[label=left:A] (O) at (0,0); \coordinate[label=above left:D] (A) at (60:2cm); \coordinate[label=right:B] (B) at (right:3cm); \begin{scope}[shift=(B)] \coordinate[label=above right:C] (C) at (60:2cm); \end{scope} \draw[line width=1pt] (O)--(B)node[midway,rotate=90]{}--(C)node[midway]{ }--(A)node[midway,rotate=90]{}--(O)node[midway]{}; \path (O)--(B) node[midway,sloped] {\(>\)}; \path (A)--(C) node[midway,sloped] {\(>\)}; \path (O)--(A) node[pos=0.7,sloped] {\(>\)}; \path (B)--(C) node[pos=0.7,sloped] {\(>\)}; \path (O)--(A) node[pos=0.8,sloped] {\(>\)}; \path (B)--(C) node[pos=0.8,sloped] {\(>\)}; \draw[line width=1pt,densely dashed] (A)--(B); \draw[line width=1pt,densely dashed] (O)--(C); \end{tikzpicture} \end{tabular} \end{tabular} \begin{multicols}{2} \textbf{Example 1}\\ Find the area of a kite with diagonals of length \(4 \text{~cm}\) and \(7 \text{~cm}\).\\ \textbf{Example 1 solution}\\ \(\begin{aligned} \text { Area } & =\frac{1}{2} \times 4 \times 7 \\ & =14 \text{~cm}^2 \end{aligned}\) \columnbreak \textbf{Example 2}\\ Find the area of a rhombus with diagonals of length \(6 \text{~cm}\) and \(8 \text{~cm}\).\\ \textbf{Example 2 solution}\\ \(\begin{aligned} \text { Area } & =\frac{1}{2} \times 6 \times 8 \\ & =24 \text{~cm}^2 . \end{aligned}\) \end{multicols}](/media/opbgelnc/7957.png)
NSW Y8 Maths Area and Perimeter Area of Kites and Rhombuses
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