# The side of an equilateral triangle is 8 cm. Find the area of a square whose perimeter is equal to the perimeter of this triangle.

June 26, 2021 | education

| First, we find what the perimeter of this triangle is equal to.

Since, according to the condition of the problem, the triangle is equilateral, its perimeter will be equal to

P = 3 * a, where a is the length of the side of the triangle.

Therefore, P = 3 * 8 = 24 (cm).

The perimeter of the square is P = 4 * a, where a is the length of the side of the square. We get:

24 = 4 * a, so a = 24: 4 = 6 (cm).

The area of the square is S = a², where a is the length of the side of the square, so the area of our square is S = 6² = 36 (cm²).

Answer: S = 36 cm².

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