Question

Find the area of a regular pentagon whose each side is $8$ cm long and the radius of whose circumscribed circle is $7$ cm.

Answer 1

Area of pentagon = $[\frac{n}{2}\times a\times \sqrt{R^2-\frac{a^2}{4}}]$ sq. units

$=[\frac{5}{2}\times 8\times \sqrt{7^2-74}]c{m}^2$

$=[20\times \sqrt{49-16}]c{m}^2$

$[20\times \sqrt{33}]c{m}^2$

$=[20\times 5.74]c{m}^2$

$=\left(114.8\right)c{m}^2$