Question

what is the area of a sectors with a radius of 12 cm and a central angle of $\frac{5pi}{4}$ radians? use the keypad to enter your answers in the boxes in terms of $pi$ (use the $pi$ symbol in each answer). area = $square$ cm²

Explanation:

Step1: Recall sector - area formula

The formula for the area of a sector of a circle is $A=\frac{1}{2}r^{2}\theta$, where $r$ is the radius of the circle and $\theta$ is the central - angle in radians.

Step2: Substitute given values

Given $r = 12$ cm and $\theta=\frac{5\pi}{4}$ radians. Substitute these values into the formula:
$A=\frac{1}{2}\times(12)^{2}\times\frac{5\pi}{4}$

Step3: Simplify the expression

First, calculate $(12)^{2}=144$. Then, $A=\frac{1}{2}\times144\times\frac{5\pi}{4}$.
$\frac{1}{2}\times144 = 72$, and $72\times\frac{5\pi}{4}=\frac{72\times5\pi}{4}=90\pi$.

Answer:

$90\pi$