Answer
The area of the semicircle on the hypotenuse is equal to the sum of the two semi-circles that have diameters of each leg of the triangle.
Work Step by Step
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.
