Answer:
[tex]\frac{x^2}{2}[/tex] 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 = [tex]\frac{x^2}{2}[/tex] ----------------(ii)
Substitute the value of a² in equation (ii) into equation (i) to get;
A = [tex]\frac{x^2}{2}[/tex]
Therefore, the area of the square is [tex]\frac{x^2}{2}[/tex] square units
