Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 3 - Section 3.4 - Arc Length and Area of a Sector - 3.4 Problem Set - Page 155: 44

Answer

6 cm$^{2}$

Work Step by Step

If $\theta$ (in radians) is a central angle in a circle with radius $r$, then the area of the sector formed by angle $\theta$ can be calculated as $A=\frac{1}{2}r^{2}\theta$. We are given that $\theta=3$ and $r=2$ cm. Therefore, $A=\frac{1}{2}(2^{2})(3)=\frac{1}{2}(4)(3)=\frac{1\times4\times3}{2}=\frac{12}{2}=6$ cm$^{2}$.
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