Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10:
ISBN 13:

Chapter 8 - Review Exercises - Page 386: 38

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.
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