Suppose you know the base of a rectangle has a length of
4 inches and a diagonal has a length of 5 inches. find the area of the rectangle.

That diagonal will split the rectangle into two triangles, with 5 inches being the hypotenuse of each. If we know that one base is 4 inches, then we can use the Pythagorean theorem to find the length of the other side of the rectangle. Let's call that other side x for now. x^2+4^2=5^2, because of the pythagorean theorum. 




So 3 is the other side of the rectangle, take that times 4 and you'll get 12 in^2.