Question

In circle G with m FGH = 54 and FG = 14 units find area of sector FGH. Round the nearest hundredth.

Answer 1

The area of a circle is calculated as follows:

`A=\pi r^2`

where r is the radius of the circle.

Substituting with r = 14, we get:

`\begin{gathered} A=\pi\cdot14^2 \\ A=\pi\cdot196 \\ A\approx615.75\text{ square units} \end{gathered}`

This area corresponds to 360° (the whole circle). To find the area that corresponds to sector FGH, we can use the next proportion:

`\frac{615.75\text{ square units}}{x\text{ square units}}=\frac{360\text{ \degree}}{54\text{ \degree}}`

Solving for x:

`\begin{gathered} 615.75\cdot54=360\cdot x \\ (33250.5)/(360)=x \\ 92.36\text{ square units }\approx\text{ x} \end{gathered}`