Question

A circle and a rectangle have the same perimeter. The sides of the rectangle are $18$ cm and $26$ cm. What is the area of the circle?

• A. $88$ $c{m}^2$
• B. $154$ $c{m}^2$
• C. $616$ $c{m}^2$
• D. $1250$ $c{m}^2$

Answer 1

The correct option is C $616$ $c{m}^2$

The sides of the rectangle are $18$ cm and $26$ cm.
Perimeter of the rectangle $=2(18+26)=88$ cm

Circumference of circle $=88$ cm.
$\Rightarrow 2\pi r=\frac{22\times 2\times r}{7}=88$

$\Rightarrow r=14cm$

Area of circle:

$\Rightarrow \pi r^2=\frac{22\times 14\times 14}{7}=616{cm}^2$