CPM Homework Help : CCG Problem 7-30

A smaller square, side length, c, rotated inside a larger square such that each vertex touches the side of the large square. A right triangle is formed along each side of the smaller square with a base of, a, a height of, b, and a hypotenuse of, c. That same triangle is positioned in each corner of the large square filling the entire space with the small square. Examine the diagram at right. Find two equivalent expressions that represent the area of the inner square.

Hint:

Area of inner $\text{square}=\left(\text{base}\right)\left(\text{height}\right)$ or large square minus $4$ triangles.

Answer:

$c^2$ or $a^2+b^2$