Question

The diagonal of a square is x units. What is the area of the square in terms of x? One-half x squared square units x squared square units 2x square units One-half x square units

Answer 1

1/2x^2 square units

Explanation:

Answer 2

`(x^2)/(2)` square units [one-half x squared square units]

Explanation:

As shown in the diagram attached to this response,

Since a square has all sides equal, let the sides of the square be each of a units.

The area, A, of the square = a x a = a²

i.e

A = a² --------------(i)

Now,

The diagonal is x units such that applying Pythagoras rule gives;

x² = a² + a²

x² = 2a²

a² =
`(x^2)/(2)` ----------------(ii)

Substitute the value of a² in equation (ii) into equation (i) to get;

A =
`(x^2)/(2)`

Therefore, the area of the square is
`(x^2)/(2)` square units