Answer:
32 ft²
Step-by-step explanation:
Given the right angle and equal sides, we have a square. The diagonal is the hypotenuse of a right triangle, so we can use the Pythagorean Theorem to calculate the side lengths, or realize that the side lengths Squared will be the area of the square.
c² = a²+b² Since a² equals b², the equation becomes c² = 2a²
8² = 2a²
64/2 = a²
32 = a², the area of the square.
The side lengths of the square are √32
about 5.657 feet. If we square that square root, we get the area of the square, 32 square feet.
