Find the area and the perimeter of a square with diagonal 24 cm.

[Take $\sqrt{2}$ = 1.41].

Diagonal of the square = 24 cm

Let a be the side of square.

By using the Pythagoras theorem,

AB² + BC² = AC²

⇒ a² + a² = (24)²

⇒ 2a² = 576

⇒ a² = $\dfrac{576}{2}$

⇒ a² = 288

⇒ a = $\sqrt{288}$

⇒ a = 12 $\sqrt{2}$

⇒ a = 12 x 1.41 = 16.92 cm

Area of the square = side²

= ($\sqrt{288}$)² cm²

= 288 cm²

Perimeter of the square = 4 x side

= 4 x 16.92 cm

= 67.68 cm

Hence, the area of the square is 288 cm² and the perimeter is 67.68 cm.