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

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Answer 1 · 2016-11-09T08:29:47

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

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
enter image source here

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 .