Circles Inscribed in Squares

When a circle is inscribed in a square , the diameter of the circle is equal to the side length of the square.

You can find the perimeter and area of the square, when at least one measure of the circle or the square is given.

For a square with side length $s$ , the following formulas are used.

Perimeter = $4s$

Area = $s^2$

Diagonal = $s\sqrt{2}$

Similarly, you can find the circumference and area of the circle , when at least one measure of the circle or the square is given.

For a circle with radius $r$ , the following formulas are used.

Circumference = $2\pi r$

Area = $\pi r^2$

When a circle is inscribed in a square, the diameter of the circle is equal to the side length of the square.

So, the side length of the square is $6$ cm.

The perimeter $P$ of a square with side length $s$ is given by $P=4s$ .

Substitute $6$ for $s$ in $P=4s$ .

$\begin{array}{l}P=4\left(6\right)\\ =24\end{array}$

The perimeter of the square is $24$ cm.