Answer:
True
Step-by-step explanation:
The area of a sector can be found in two ways:
First. With a formula in degrees.
[tex]A=\frac{\pi r^2 \alpha^{\circ}}{360^{\circ}}[/tex]
Second. With a formula in radians.
[tex]A=\frac{r^2 \beta }{2}[/tex]
For example, for a sector α = 180° (β = π). we have:
[tex]A=\frac{\pi r^2 \alpha^{\circ}}{360^{\circ}} \therefore A=\frac{\pi r^2 180^{\circ}} {360^{\circ}} \therefore A=\frac{\pi r^2}{2}\\ \\ \\ A=\frac{r^2 \beta }{2} \therefore A=\frac{r^2 \pi }{2} \therefore A=\frac{\pi r^2}{2}[/tex]
As you can see, from the two forms we have found out that if you want to find the area of a sector, you multiply the area of the circle by the fraction of the circle covered by that sector, because 180° (π) represents half a circle.
