Question

The length of a chain used as the boundary of a semicircular park is 90 m. Find the area of the park.

Answer 1

Let the radius of the park be r m.
Thus, we have:
$$\begin{gathered} \mathrm{\pi }r+2r=90 \\ \Rightarrow r(\mathrm{\pi }+2)=90 \end{gathered}$$

$$\begin{gathered} \Rightarrow r=\frac{90}{\mathrm{\pi }+2} \\ \Rightarrow r=\frac{90}{{\displaystyle \frac{22}{7}}+2} \\ \Rightarrow r=\frac{90\times 7}{36} \\ \Rightarrow r=17.5 \end{gathered}$$

Now,
Area of the park = $\frac{1}{2}\mathrm{\pi }{r}^2$
$$\begin{gathered} =\frac{1}{2}\times \frac{22}{7}\times 17.5\times 17.5 \\ =481.25{\mathrm{m}}^2 \end{gathered}$$
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