Question

The length of a chain used as the boundary of a semicircular park is 108 m. Find the area of the park.

Answer 1

Let the radius of the park be r.
Length of chain = Perimeter of the semicircular park
⇒ 108 = Length of the arc + Diameter
$$\begin{gathered} \Rightarrow 108=\frac{1}{2}\times 2\mathrm{\pi }r+2r \\ \Rightarrow 108=r\left(\frac{22}{7}+2\right) \\ \Rightarrow 108=\frac{36}{7}r \\ \Rightarrow r=21\mathrm{m} \end{gathered}$$
Now, Area of park$=\frac{1}{2}\mathrm{\pi }{r}^2=\frac{1}{2}\times \frac{22}{7}\times {\left(21\right)}^2=693{\mathrm{m}}^2$
Hence, the area of the park is 693 m² .