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

We know that the diagonal of a square is given by side*sqrt(2). So, if the diagonal is 12sqrt(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 4side. So, the perimeter of this square is 412 = 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 48/3 = 16 cm.

Step 4: Find the area of the equilateral triangle

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