Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10: 9781285195698
ISBN 13: 978-1-28519-569-8

Chapter 8 - Section 8.5 - More Area Relationships in the Circle - Exercises - Page 379: 4


(a) $P = 2r+\pi~r$ (b) $A = \frac{1}{2}~\pi~r^2$

Work Step by Step

(a) Since the radius is $r$, the diameter is $2r$ We can find the length $L$ of half the circumference: $L = \frac{1}{2}~\pi~d$ $L = \frac{1}{2}~\pi~(2r)$ $L = \pi~r$ We can find the total perimeter of the region: $P = 2r+\pi~r$ (b) We can find the area of half of the full circle: $A = \frac{1}{2}~\pi~r^2$
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