Question

The circumference of the circle is equal to the perimeter of a square. If area of the square is $484sqm$, then find the area of the circle.

Answer 1

Let side of square$=xm$
then perimeter of square $4\times x$
and area of square$=x^2$
According to question
Area of square$=484sqm$
$x^2=484$
$x=\sqrt{484}$
$=22m$
Perimeter of square$=4x=4\times 22=88m$
Let radius of circle is r
circumference of circle = perimeter of square
$\Rightarrow 2\pi r=88$
$\Rightarrow 2\times \frac{22}{7}\times r=88$
$r=\frac{88\times 7}{2\times 22}=14m$
Thus, area of the circle$=\pi r^2$
$=\frac{22}{7}\times 14\times 14=616sqm.$
Thus, area of the circle$=616sqm.$