Question

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

Answer 1

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 `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)=sqrt2`

Now as side of square is `10`, radius of circle would be `10/sqrt2`,

and perimeter of a circle of radius `r` being `2pir`,

perimeter of circle circumscribed about the square would be

`2pixx10/sqrt2=10xxpixxsqrt2`

= `10xx3.1416xx1.4142=44.4285` in .