The side of an equilateral triangle is 12cm. Find the area of a square whose perimeter is equal to the perimeter of this triangle.

By condition, an equilateral triangle is given, we find its perimeter by the formula:
R tr. = 3 * a = 3 * 12 = 36 (cm).
According to the problem statement, a square has the same perimeter as a triangle. We can find the side of the square from the perimeter formula:
R sq. = 4 * a → a = P square. / 4 = 36/4 = 9 (cm).
The side is known, we find the area of the square using the formula:
S sq. = a² = 9 * 9 = 81 (cm²).
Answer: the area of the square is 81 cm².