# Given that the area of a square inscribed in a circle is 64 cm^2, how do you find the area of the circle?

Jun 9, 2015

area of the circle  =color(purple)( 100.48 cm^2

#### Explanation:

Area of the square $= 64 c {m}^{2}$
So the side of this square  =color(purple)( sqrt64 = 8cm
And the diagonal of this square  = sidesqrt2 =color(purple)( 8sqrt2

Given that the square is inscribed inside the circle , the diagonal of this square $=$ the diameter $\left(d\right)$ of the circle.

$\textcolor{p u r p \le}{8 \sqrt{2}} = d$
So, the radius , color(purple)(r = 4sqrt2

Now , the area of the circle $= \pi {\left(r\right)}^{2}$
 = 3.14 xx color(purple)((4sqrt2)^2
 = 3.14 xx color(purple)(16 xx 2

 =color(purple)( 100.48 cm^2