Find the area of a square if its perimeter is equal to the perimeter of a rectangle with sides of 8 cm and 10 cm.

To solve this problem, remember that the perimeter of a rectangle is the sum of the lengths of all its sides. Since in a rectangle the opposite sides are equal, then P = 2 * (a + b), where a is the length, b is the width. Knowing that the length is 10 cm and the width is 8 cm, we calculate the perimeter of the rectangle.
P = 2 * (8 + 10) = 2 * 18 = 36 centimeters.
Since all sides of a square are equal, then its perimeter is P = 4a, where a is its side. We calculate the side of the square, knowing that the perimeter is 36 cm.
a = 36/4 = 9 cm.
The area of a square is equal to the square of its side. S = a ^ 2.
S = 9 * 9 = 81 cm ^ 2.
Answer: 81 cm ^ 2.