Question

An equilateral triangle and a square have equal perimeters. The side of the triangle measures 8cm. What is the area of the square, in square centimeters?

Answer 1

Area of the square = 36 square cm

Explanation:

Given:

The perimeter of an equilateral triangle = the perimeter of a square

In an equilateral triangle, all sides are equal

Each side of the equilateral triangle = 8cm

Perimeter of the equilateral triangle = 3 * 8cm

Perimeter of the equilateral triangle = 24cm

Since, perimeter of square = perimeter of an equilateral triangle

Perimeter of a square = 24cm

We need to find each side of the square

Perimeter of a square = 4s

24 = 4s

Divide both side by 4

24/4 = 4s/4

s = 6cm

Since the length of each side of the square is 6cm

Therefore, area = l^2

Area = 6 * 6

Area of a square = 36 square cm