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

$1232c{m}^2$

$\text{Given perimeter of a semicircle = 144 cm}$
$\text{Let r be the radius of the semicircle.}$
$\Rightarrow r(\pi +2)=144$
$\Rightarrow r(\frac{22}{7}+2)=144$
$\Rightarrow r\left(\frac{22+14}{7}\right)=144$
$\Rightarrow r\times \frac{36}{7}=144\Rightarrow r=28cm$
$\text{Area of semicircle}$
$=\frac{1}{2}\pi r^2=\frac{1}{2}\times \frac{22}{7}\times 28\times 28$
$=1232c{m}^2$