## Elementary Geometry for College Students (6th Edition)

We know: $a^2 +b^2 =c^2$ Since each radius is half of the length of the side, we obtain an equal expression: $(a/2)^2 + (b/2)^2 = (c/2)^2$ We multiply everything by pi/2: $\pi/2 \times(a/2)^2 + \pi/2 \times(b/2)^2 =\pi/2 \times (c/2)^2$ Thus, we see that the sum of the areas of the two smaller semicircles equals the area of the larger semi-circle.