A square and an equilateral triangle have an equal perimeter. If the diagonal of the square is 12√2 cm, then the area of a triangle is ________.

In a Square,

Length of diagonal = √2(side)

∴ The perimeter of square = 4 × side

∴ Perimeter of Square = 4 × 12 = 48 cm.

The perimeter of triangle = 3 × a, where a is the side of the triangle.

As the square and an equilateral triangle have an equal perimeter.

∴ 3 × a = 48

⇒ a = 16cm.

Also, Area of equilateral triangle =

=

∴ Area of an equilateral triangle is .