Question

find the area of the larger sector. round to the nearest tenth. 255° 13.4 miles area = ?miles²

Explanation:

Step1: Recall sector - area formula

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

Step2: Identify values

The radius $r = 13.4$ miles and the central - angle of the larger sector $\theta=360^{\circ}-255^{\circ}=105^{\circ}$.

Step3: Substitute values into the formula

$A=\frac{105^{\circ}}{360^{\circ}}\times\pi\times(13.4)^{2}$.
First, calculate $(13.4)^{2}=179.56$. Then, $\frac{105}{360}\times\pi\times179.56$.
$\frac{105}{360}\approx0.2917$.
$A = 0.2917\times\pi\times179.56$.
$A\approx0.2917\times3.14\times179.56$.
$A\approx0.2917\times563.82$.
$A\approx164.5$.

Answer:

$164.5$ miles$^{2}$