# How do you find the circumference of a circle circumscribed about a square with perimeter 40 in?

Nov 9, 2016

Perimeter of circle circumscribed about the square would be $44.4285$ in .

#### Explanation:

As all the sides of a square are equal,

if its perimeter is $40$, each side is $\frac{40}{4} = 10$ in.

Now look at the following figure of a circle circumscribed about a square

If the radius of a circle is $1$ unit, the side of square by Pythagoras theorem is $\sqrt{{1}^{2} + {1}^{2}} = \sqrt{1 + 1} = \sqrt{2}$

Now as side of square is $10$, radius of circle would be $\frac{10}{\sqrt{2}}$,

and perimeter of a circle of radius $r$ being $2 \pi r$,

perimeter of circle circumscribed about the square would be

$2 \pi \times \frac{10}{\sqrt{2}} = 10 \times \pi \times \sqrt{2}$

= $10 \times 3.1416 \times 1.4142 = 44.4285$ in .