A square and an equilateral triangle have equal perimeters. If the diagonal of the square is 12√2 cm,find the area of the triangle

Step 1: Find the side of the square

The diagonal of a square is given by the formula √2 * side. So, if the diagonal is 12√2 cm, the side of the square is 12 cm.

Step 2: Find the perimeter of the square

The perimeter of a square is given by the formula 4 * side. So, if the side is 12 cm, the perimeter of the square is 48 cm.

Step 3: Find the side of the equilateral triangle

Since the perimeters of the square and the equilateral triangle are equal, the side of the equilateral triangle is 48 cm / 3 = 16 cm.

Step 4: Find the area of the equilateral triangle

The area of an equilateral triangle is given by the formula (sqrt(3) / 4) * side^2. So, if the side is 16 cm, the area of the equilateral triangle is (sqrt(3) / 4) * 16^2 = 64sqrt(3) cm^2.