Question

in circle m with m∠lmn = 156° and lm = 19, find the area of sector lmn. round to the nearest hundredth. answer attempt 1 out of 2 units²

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 in degrees and $r$ is the radius of the circle.

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

We are given that $\theta = 156^{\circ}$ and the radius $r = LM=19$.

Step3: Substitute the values into the formula

$A=\frac{156^{\circ}}{360^{\circ}}\times\pi\times(19)^{2}$.
First, calculate $(19)^{2}=361$. Then, $\frac{156}{360}\times\pi\times361=\frac{13}{30}\times\pi\times361$.
$A=\frac{13\times361\pi}{30}=\frac{4693\pi}{30}\approx\frac{4693\times3.14159}{30}$.
$4693\times3.14159 = 14743.58187$.
$\frac{14743.58187}{30}\approx491.45$.

Answer:

$491.45$