Question

find the area of the blue shaded region. 8.35 ft 100° area = ? ft round to the nearest tenth

Explanation:

Step1: Recall the formula for the area of a sector

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

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

We are given that $r = 8.35$ ft and $\theta=360 - 100=260^{\circ}$.

Step3: Substitute the values into the formula

$A=\frac{260}{360}\times\pi\times(8.35)^{2}$.
First, calculate $(8.35)^{2}=69.7225$.
Then, $\frac{260}{360}\times\pi\times69.7225=\frac{13}{18}\times\pi\times69.7225$.
$\frac{13\times\pi\times69.7225}{18}\approx\frac{13\times3.14\times69.7225}{18}$.
$13\times3.14\times69.7225 = 13\times219.92865=2859.07245$.
$\frac{2859.07245}{18}\approx158.8$.

Answer:

$158.8$ ft²