find the area of the shaded sector. round to the nearest tenth. 167° 17.8 yd area = ?yd²

Answer:

$469.7$

Explanation:

Step1: Recall area - of - a - sector formula

$A=\frac{\theta}{360}\times\pi r^{2}$, where $\theta$ is the central angle and $r$ is the radius.

Step2: Identify values

$\theta = 167^{\circ}$, $r = 17.8$ yd.

Step3: Substitute values into formula

$A=\frac{167}{360}\times\pi\times(17.8)^{2}$.

Step4: Calculate

First, $(17.8)^{2}=316.84$. Then $\frac{167}{360}\times\pi\times316.84\approx\frac{167}{360}\times3.14\times316.84$. $\frac{167}{360}\times3.14\times316.84=\frac{167\times3.14\times316.84}{360}\approx469.7$ yd².