The diagonal of a square unit is x units. what is the area of the square in terms of x

Area of square = a^2 
but
a^2 = d^2 / 2 = x^2 / 2

so area = x^2/2

answer is A. x^2 / 2 or 1/2 (x)^2

The diagonal of a square is:

d^2=s^2+s^2

d^2=2s^2  we are told that d=x  so

x^2=2s^2

s^2=(x^2)/2

And since the area of a square is s^2, the area of this square is:

(x^2)/2

Or as it is shown in your answer choices...

(1/2)x^2 square units  (the top answer :P)

Here is my answer, i'm sorry if you didn't understand my explanation