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 of $\theta$ and $r$

We are given that $\theta = 255^{\circ}$ and $r = 13.4$ miles.

Step3: Substitute values into the formula

$A=\frac{255^{\circ}}{360^{\circ}}\times\pi\times(13.4)^{2}$
First, calculate $\frac{255}{360}=\frac{17}{24}$. Then, $(13.4)^{2}=179.56$.
So, $A=\frac{17}{24}\times\pi\times179.56$.
$A=\frac{17\times\pi\times179.56}{24}$.
$A=\frac{17\times3.14\times179.56}{24}$ (using $\pi\approx3.14$).
$17\times3.14 = 53.38$, and $53.38\times179.56=9586.2128$.
$A=\frac{9586.2128}{24}\approx399.4$.

Answer:

$399.4$ miles$^{2}$