A square and a rectangle have the same perimeter. The length of the rectangle is 8cm

A square and a rectangle have the same perimeter. The length of the rectangle is 8cm and the width is 4cm. Find the area of the square.

Let’s find the perimeter of this rectangle:

P = 8 cm + 8 cm + 4 cm + 4 cm = 24 cm.

Since the perimeter of the rectangle and the square are equal, therefore, we can find the side of the square, given that all its sides are equal to each other:

24 cm: 4 = 6 cm.

The area of a square is calculated as the square of the length of its side. We calculate the area of a square with a side of 6 cm:

S = 62 = 36 cm2.

Answer: S = 36 cm2.