Question

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

1/2x2 square units
x2 square units
2x square units
1/2x square units

Answer 1

`(1)/(2)x^2` square units

Explanation:

The simple formula we need here is:

`d=s√(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√(2) \\x=s√(2) \\s=(x)/(√(2))`

Now,

we know area of square is
`s^2`

We know s, and now we find area

Area =
`s^2\\((x)/(√(2)))^2\\(x^2)/(2)\\(1)/(2)x^2`

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