Question

in circle l with (mangle klm = 78^{circ}) and (kl = 4), find the area of sector klm. 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 measure in degrees and $r$ is the radius of the circle.

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

We are given that $\theta = 78^{\circ}$ and $r = KL=4$.

Step3: Substitute the values into the formula

$A=\frac{78^{\circ}}{360^{\circ}}\times\pi\times4^{2}=\frac{78}{360}\times\pi\times16$.

Step4: Calculate the value

First, $\frac{78}{360}\times16=\frac{78\times16}{360}=\frac{1248}{360}=\frac{104}{30}=\frac{52}{15}$. Then $A = \frac{52}{15}\pi$.
Using $\pi\approx3.14159$, we have $A=\frac{52}{15}\times3.14159\approx10.89$.

Answer:

$10.89$