Find the area and perimeter of a square plot of land whose diagonal is 15 m. Give your answer correct to two decimal places.

Given:

Diagonal of the square = 15 m

Let 'a' be the length of side of the square.

Using the Pythagoras theorem in square,

⇒ Diagonal² = side² + side²

⇒ 15² = 2 × side²

⇒ 225 = 2 × a²

⇒ a² = $\dfrac{225}{2}$

⇒ a² = 112.5

⇒ a = $\sqrt{112.5}$ = 10.606 m.

Area of square = side² = a²

= 112.50 m².

Perimeter = 4 × side

= 4 × 10.606 = 42.42 ≈ 42.42 m.

Hence, area = 112.50 m² and perimeter = 42.42 m.