Question

What is the area of a square if the half of the diagonal is 6

Answer 1

72

Explanation:

Cut the square into two equal triangles along the diagonal

You know that half of the diagonal is 6 so multiply that by 2 to get 12 which is the hypotenuse of your triangles

Then use the pythagorean theorem to solve for the sides

a^2 + b^2 = 12^2

a^2 + b^2 = 144

Since the original shape was a square both sides a and b are equal

a^2 = b^2

a^2 + a^2 = 144

2a^2 = 144

a^2 = 144/2

a^2 = 72

a =
`√(72)`

Since a = b then a =
`√(72)` =b

Multiply both sides a and b to get the area of the square

`√(72)` *
`√(72)` = 72