The area of the rectangle is 640m2, and the side length is 40m.

The area of the rectangle is 640m2, and the side length is 40m. Find the area of a square whose perimeter is equal to the perimeter of the rectangle.

The area S of the rectangle is 640 m2.
The length a of one side of the figure is 40 meters.
The perimeter of the square is the same as the perimeter of the rectangle.
Let’s calculate the width b of the rectangle:
b = S: a = 640: 40 = 16 meters.
Find the perimeter of the quadrangle:
P = 2a + 2b = 2 * 40 + 2 * 16 = 80 + 32 = 112 centimeters.
All sides of the square are equal in length.
Find the side of the square:
112: 4 = 28 centimeters.
Let’s calculate the area of this figure:
28 * 28 = 784 cm2.
Answer: the area of the square is 784 cm2.