Question

A rectangle ABCD is constructed in circle where length of the rectangle is the diameter AB of the circle and BC is the breadth and also the radius of the circle, find the area of rectangle if perimeter of circle is 44 cm

• A. 49 $c{m}^2$
• B. 98 $c{m}^2$
• C. 128 $c{m}^2$
• D. 196 $c{m}^2$

Answer 1

The correct option is B 98 $c{m}^2$

Diameter = AB = length of the rectangle.
Radius = AB = AD = OP

circumference of circle = pi$\times$diameter

Diameter = $\frac{circumference}{\pi }$
= $\frac{44}{\pi }$
Diameter = $\frac{44\times 7}{22}$ = 14 cm

Diameter = 2$\times$radius

Hence radius = $\frac{diameter}{2}$ = $\frac{14}{2}$ = 7 cm

area of rectangle = length $\times$breadth
= AB$\times$BC
= 14$\times$7
= 98$c{m}^2$