Question

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

Answer 1

The length of a chain used as the boundary of a semicircular park = $108cm$
i.e. circumference of a semicircular park = $108cm$
Let the radius of semicircular park =$r$
Which implies,
$\Rightarrow \pi r+2r=108$
$\Rightarrow (\frac{22}{7}+2)r=108$
$\Rightarrow (\frac{22+14}{7})r=108$
$\Rightarrow \frac{36}{7}r=108$
$\therefore r=\frac{108\times 7}{36}=21cm$
Now,
Area of a semicircular park = $\frac{1}{2}\pi r^2=\frac{1}{2}\times \frac{22}{7}\times 21\times 21=\frac{1}{2}\times 1386=693$.
Therefore, Area of the park is $693m^2$.