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

Answer:

$\frac{x^2}{2}$ square units        [one-half x squared square units]

Step-by-step 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 = $\frac{x^2}{2}$           ----------------(ii)

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

A = $\frac{x^2}{2}$

Therefore, the area of the square is $\frac{x^2}{2}$ square units

Answer 2

Answer:

1/2x^2 square units

Step-by-step explanation: