Question

find the area of this sector if ( r = \frac{9}{2} ) and ( \theta = \frac{5pi}{6} ) radians.

( \frac{?pi}{} ) sq units

Explanation:

Step1: Recall the formula for the area of a sector

The formula for the area of a sector is \(A=\frac{1}{2}r^{2}\theta\), where \(r\) is the radius and \(\theta\) is the central angle in radians.

Step2: Substitute the given values into the formula

Given \(r = \frac{9}{2}\) and \(\theta=\frac{5\pi}{6}\).
First, calculate \(r^{2}\): \(r^{2}=(\frac{9}{2})^{2}=\frac{81}{4}\).
Then, substitute into the formula: \(A=\frac{1}{2}\times\frac{81}{4}\times\frac{5\pi}{6}\).

Step3: Simplify the expression

$$
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$$

Answer:

\(\frac{135}{16}\pi\)