Question

In circle F with mZEFG = 144 and EF 144 and EF = 14 units find area of sector EFG. Round to the nearest hundredth. G F E

Answer 1

First, we need to calculate the area of the whole circle.

The area of a circle is computed as follows:

`A=\pi r^2`

The radius of circle F is EF = 14.

`\begin{gathered} A=\pi\cdot14^2 \\ A=615.75 \end{gathered}`

This area corresponds to 360°. To find the area that corresponds to 144°, we can use the next proportion:

`(615.75)/(x)=\frac{360\text{ \degree}}{144\text{ \degree}}`

Solving for x,

`\begin{gathered} 615.75\cdot144=360\cdot x \\ (615.75\cdot144)/(360)=x \\ 246.3=x \end{gathered}`

The area of sector EFG is 246.3