Question

If the perimeter of a semi circle is 144 cm, what is its area?

• A. $1232c{m}^2$
• B. $1223c{m}^2$
• C. $1322c{m}^2$
• D. $1323c{m}^2$

Answer 1

The correct option is A $1232c{m}^2$

Given perimeter of a semicircle = 144 cm
Let $r$ be the radius of the semicircle.

Perimeter of semicircle = $2r$ (Straight line diameter) + $\pi r$ (Curved surface)

$\Rightarrow \pi r+2r=144$

$\Rightarrow r(\pi +2)=144$

$\Rightarrow r(\frac{22}{7}+2)=144$

$\Rightarrow r\left(\frac{22+14}{7}\right)=144$

$\Rightarrow r\times \frac{36}{7}=144\Rightarrow r=28cm$

Area of semicricle

$=\frac{1}{2}\pi r^2=\frac{1}{2}\times \frac{22}{7}\times 28\times 28$

$=1232c{m}^2$