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:

$\begin{gathered} 615.75\cdot54=360\cdot x \\ \frac{33250.5}{360}=x \\ 92.36\text{ square units }\approx\text{ x} \end{gathered}$