what is the area of sector gph? the area of sector gph is square yards. (type an exact answer in terms of π.)

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 the values of $\theta$ and $r$

From the problem, $\theta = 40^{\circ}$ and $r = 15$ yd.

Step3: Substitute the values into the formula

$A=\frac{40^{\circ}}{360^{\circ}}\times\pi\times(15)^{2}$. First, simplify $\frac{40}{360}=\frac{1}{9}$. Then, $(15)^{2}=225$. So, $A=\frac{1}{9}\times\pi\times225$.

Step4: Calculate the area

$A = 25\pi$ square yards.

Answer:

$25\pi$