Question

this exercise involves the formula for the area of a circular sector. find the area a of the sector shown in each figure. (a)

Explanation:

Step1: Recall sector - area formula

The formula for the area of a circular sector is $A=\frac{\theta}{360^{\circ}}\times\pi r^{2}$, where $\theta$ is the central - angle measure in degrees and $r$ is the radius of the circle.

Step2: Identify values of $\theta$ and $r$

From the figure, $\theta = 65^{\circ}$ and $r = 5$.

Step3: Substitute values into the formula

$A=\frac{65^{\circ}}{360^{\circ}}\times\pi\times5^{2}=\frac{65}{360}\times25\pi=\frac{65\times25\pi}{360}=\frac{325\pi}{72}\approx14.2$.

Answer:

$\frac{325\pi}{72}\approx14.2$