What is the diagonal of a square whose area is 36?

First you want to find the lengths of the square. The formula for area is b × h, but because it's a square (and the base is the same as the height), the area can be expressed as b2. So if b2 = 36, then √36 = b. Therefore, b = 6.

If you draw the diagonal in the square and make a triangle, you can use the two sides you do know to figure out the third side of the triangle using the Pythagorean theorem.

62 + 62 = c2

72 = c2

√72 = c

c ≈ 8.49