## Geometry: Common Core (15th Edition)

Published by Prentice Hall

# Chapter 10 - Area - 10-7 Areas of Circles and Sectors - Practice and Problem-Solving Exercises - Page 663: 15

#### Answer

$\dfrac{169}{6} \pi \ m^2$

#### 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 $r=13 \ m (\because r=\dfrac{d}{2}=\dfrac{26}{2}=13)$ and $Measure \ of \ the \ arc=180\circ-120\circ=60^{\circ}$ Plug the data in the equation (1) to obtain: $A=\pi (13)^2 \times \dfrac{60^{\circ}}{360^{\circ}}$ Therefore, we get , $Area=\dfrac{169}{6} \pi \ m^2$

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