Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 10 - Area - 10-7 Areas of Circles and Sectors - Practice and Problem-Solving Exercises - Page 663: 17


$12 \pi \ ft^2$

Work Step by Step

Let $A$ be the area of a sector of a circle . The area $(A)$ of a sector of a circle whose radius is $r$ is given by: $A=\pi r^2 \times \dfrac{Measure \ of \ the \ arc}{360^{\circ}}...(1)$ We are given that radius $r=4 \ ft $ and $Measure \ of \ the \ arc=360^{\circ}-90^{\circ}=270^{\circ}$ Plug the data in the equation (1) to obtain: $A=\pi (4)^2 \times \dfrac{270^{\circ}}{360^{\circ}}$ Therefore, we get , $Area=12 \pi \ ft^2$
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