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

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

1. Find the unknown side of the rectangle by dividing its area by the length of the known side:
640/40 = 16 m.
2. Find the perimeter of the rectangle by adding the doubled value of its adjacent sides:
Perimeter = 16 * 2 + 40 * 2 = 32 + 80 = 112 m.
3. Find the side of the square, if its perimeter is 112 meters, for this we divide the perimeter into 4 sides:
112/4 = 28 m.
4. Find the area of the square by the formula S = a * a, where S is the area of the square, and is its side:
S = 28 * 28 = 784 m2.
Answer: the area of the square is 784 m2.