Question

What is the area of the square with diagonals of length 6?

Answer 1

Here's a diagram:

Let the sides of the square be `x`.

As you probably already know, all 4 sides of a square are equal in length. Also, you will know that the 4 interior angles in a square all are right, or measure `90˚`. Hence, we can use pythagorean theorem to determine the value of `x`.

Let `a` and `b` be the sides of the square and `c` be the diagonal.

`a^2 + b^2 = c^2`

`x^2 + x^2 = 6^2`

`2x^2 = 36`

`x^2 = 18`

`x = sqrt(18)`

`x = 3sqrt(2)" units"`

All that remains to do is to apply the formula for area of a square, `A = s^2`, where `x = s`.

`A = (3sqrt(2))^2 = 9(2) = 18`

Thus, the area of the square is `18" units"^2`.

Hopefully this helps!