Question

The area of a semicircle is 1925 cm2.

Calculate its perimeter (in cm).​

Answer 1

Given ,

Area of semicircle = 1925 cm²

It can be written as

$\star \: \sf \frac{\pi {r}^{2} }{2} = 1925 \: \: {cm}^{2}$

From this , we obtain

$\sf \implies \frac{ \cancel{22} \times {r}^{2} }{7 \times \cancel{2} } = 1925 \\ \\ \sf \implies \frac{11 \times {r}^{2} }{7} = 1925 \\ \\ \sf \implies 11 \times {r}^{2} = 13475 \\ \\ \sf \implies {r}^{2} = 1225 \\ \\ \sf \implies r = \sqrt{1225} \\ \\ \sf \implies r = 35$

Thus , the radius of the circle is 35 cm

We know that , the perimeter of semicircle is given by

$\sf \fbox{ \fbox{Perimeter \: of \: semicircle = \pi(r)}}$

$\sf = \frac{22}{7} \times 35 \\ \\ \sf = 22 \times 5 \\ \\ \sf = 110 \: cm$

Therefore , the perimeter of the circle is 110 cm