If the diagonal of the square is 8 feet what is the area of the square

32

Step-by-step explanation:

You have to use pythagorean theorem for this, where a and b represent the 2 sides while c represents the hypoteneuse.

a²+b²=c²

If the diagonal of a square is 8, it divides the square into 2 triangles, both with a hypoteneuse of 8. Since it is a square, that means the other 2 sides will have equal lengths. So input 8 into the equation:

a²+b²=8²

a²+b²=64

Then you can change a and b into the same variable, since you know they will be equal due to you working with a square.

a²+a²=64

simplify: 2a²=64

divide both sides by 2: a²= 32

square root both sides: a =

then you know the length of each side is

to find the area of a square, you must multiply both sides by each other, so do *, which will give you 32 since you are essentially doing this:

in which the square and square root cancel out.