Question

The diagonal of a square is x units. What is the area of the square in terms of X?

Answer 1

Answer:

$\frac{1}{2}x^2$ square units

Step-by-step explanation:

The simple formula we need here is:

$d=s\sqrt{2}$

Where

d is length of diagonal

s is length of side of square

Let's find side length of square from information given:

$d=s\sqrt{2} \\x=s\sqrt{2} \\s=\frac{x}{\sqrt{2}}$

Now,

we know area of square is  $s^2$

We know s, and now we find area

Area = $s^2\\(\frac{x}{\sqrt{2}})^2\\\frac{x^2}{2}\\\frac{1}{2}x^2$

The first answer choice is right, 1/2x^2 sq. units.