Question

A wire when bent in the form of a square encloses an area of 484 cm². If the same wire is bent into the form of a circle, find the area of the circle. 

Answer 1

Area of the square = 484 cm² 

Side of the square = ${\displaystyle \sqrt{484}}$ = 22 cm

Perimeter of the square = 4 x 22 = 88 cm 

Perimeter of square = perimeter of circle 

21 π r = 88 

r = ${\displaystyle 88\times \frac{7}{22}\times \frac{1}{2}}$

r = 14 cm

Radius of circle = 14 cm 

Area of cirde = 11π r² 

${\displaystyle =\frac{22}{7}\times 14\times 14}$

= 616 cm²

Hence, area of the circle = 616 cm²