The figure below is made up of a square and 4 semicircles. The perimeter of the figure is $20\pi$ cm. What is the perimeter of the square? Ans : ___ cm

1. Relate the perimeter of the figure to the semicircles

The perimeter of the figure consists of the arc lengths of the 4 semicircles. The straight edges of the square are inside the figure and do not contribute to the perimeter.
Let the side length of the square be $d$. This is also the diameter of each semicircle.
Perimeter of 4 semicircles = $4 \times \frac{1}{2} \times \pi d = 2\pi d$

2. Find the diameter of the semicircles (side of the square)

Given the perimeter is $20\pi$ cm:
$2\pi d = 20\pi$
$d = 10$ cm

3. Calculate the perimeter of the square

The side of the square is $10$ cm.
Perimeter of the square = $4 \times 10 = 40$ cm