Problem Solving and Modelling - Questions
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A map is drawn to scale of \(1:15000\). A park drawn on a map contains a lake that has an area of \(12~\text{cm}^2\). Calculate the actual area of the lake in hectares, given that \(1\,\text{hectare} = 10000~\text{m}^2\)
\begin{align}
&\text{Given the area of the lake }=12 \mathrm{~cm}^{2}\\
&\text{Let the length }L=4 \mathrm{~cm}\\
&\text{and the breadth } =3 \mathrm{~cm}\\
&\text{Scale }=1:15000\\
&\begin{aligned}
\therefore \text { Actual length } L_{A} &=4 \times 15000 \\ &=60000 \mathrm{~cm} \\ &=600 \mathrm{~m}\\
\text{Actual breadth }B_{A}&=3 \times 15000\\
&=45000 \mathrm{~cm} \\
&=450 \mathrm{~m}\\
\therefore \text { Actual area } &=600 \times 450 \mathrm{~m}^{2} \\
&=270000 \mathrm{~m}^{2} \\
&=27 ~\text{ha}
\end{aligned}
\end{align}
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