Question

The area of a semicircle is 32π cm .Work out the perimeter of the semicircle.
Give your answer in terms of π.

Answer 1

$\huge\mathbb{\underline{SOLUTION:-}}$

$\sf\underline{\blue{\:\:\: Given\:\:\:}}$

$\sf\:\:\bullet Area\:of\: Semicircle=32\pi cm{}^{2}$

$\sf\underline{\red{\:\:\: To\:Find\:\:\:}}$

We have to find the perimeter of semicircle

$\boxed{\sf{Area\:of\: semicircle=\dfrac{\pi r{}^{2}}{2}}}$

• First find the radius of semicircle

$\sf:\implies \dfrac{\pi r{}^{2}}{2}=32\pi\\ \\ \sf:\implies \cancel{\pi} r{}^{2}=32\cancel{\pi}\times 2\\ \\ \sf:\implies r{}^{2}=64\\ \\ \sf:\implies r=\sqrt{64}\\ \\ \sf:\implies r= 8cm$

• Now the Perimeter

$\boxed{\sf{Perimeter\:of\: semicircle=\pi r+2r}}$

• Radius =8cm

$\sf:\implies Perimeter=\pi \times 8+2\times 8\\ \\ \sf:\implies Perimeter=(8\pi +16)cm$

$\sf\underline{\boxed{\sf{Perimeter\:of\: semicircle=(8\pi +16)cm}}}$

Answer 2

Answer : 8π + 16 cm

$\rule{100}2$

Given :

• Area of semicircle = 32π cm.

To Find :

• Perimeter of the semicircle.

Solution :

We know that, Area of semicircle $\tt =\dfrac{\pi\:r^2}{2}$

Hence,

$\tt \dfrac{\pi\:r^2}{2} = 32\pi$

$\tt \implies \pi \times r^2 = 32 \pi\times 2$

==> $r^2= {32}\times {2}$

==> $r^2 =64$

==> $r =\sqrt{64}$

$\tt \therefore r = 8$

Radius of the semicircle is 8 cm.

Now,

$\sf\red Perimeter\:of\:semicircle\:=\pi\times r+ dismeter$

$\sf = \pi \times 8 + 2\times 8$

$\sf = 8\pi + 16$

Therefore,

Perimeter of the given semicircle is 8π + 16 cm.

$\rule{200}2$