Find the area of a rectangle with a side of 8 cm, which has the same perimeter as a square with a side of 10 cm.

1) Find the perimeter of a square with a side of 10 cm:

10 * 4 = 40 (cm) – the perimeter of the square.

This means that the perimeter of the rectangle is also 40 cm.

Formula for finding the perimeter of a rectangle:

P = 2 * (a + b).

Let us express the width from the formula:

a = (P – 2b) / 2.

2) Find the width of the rectangle:

(40 – 8 * 2): 2 = (40 – 16): 2 = 12 (cm) – the width of the rectangle.

The formula for finding the area of a rectangle:
S = a * b, where a is the width, b is the length of the rectangle.

3) Find the area:

8 * 12 = 96 (cm ^ 2) – area.

Answer: the area of the rectangle is 96 cm ^ 2.