Question

18.

The length of the diagonal of a square is 12 cm. What is the area of the
square?
​

Answer 1

Answer: 72 sq. in.

Explanation:

A = a^2

D = √2 a

Solving for A

A = 1/2 x d^2

= 1/2 x 12^2

= 1/2 x 144

= 72 sq in

Answer 2

72 cm²

Explanation:

The diagonal of the square divides the square into 2 right triangles.

let the legs of the triangle be x , then using Pythagoras' identity.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

The hypotenuse of the triangle is the diagonal, thus

x² + x² = 12²

2x² = 144 ( divide both sides by 2 )

x² = 72 ( take the square root of both sides )

x =
`√(72)`

The area of the square = x² = (
`√(72)` )² = 72 cm²