Question

True or false? to find the area of a sector, you multiply the area of the circle by the fraction of the circle covered by that sector.
a.true

Answer 1

Answer:

ITs true

Step-by-step explanation:

just did the test

Answer 2

Answer:

True

Step-by-step explanation:

The area of a sector can be found in two ways:

First. With a formula in degrees.

$A=\frac{\pi r^2 \alpha^{\circ}}{360^{\circ}}$

Second. With a formula in radians.

$A=\frac{r^2 \beta }{2}$

For example, for a sector α = 180° (β = π). we have:

$A=\frac{\pi r^2 \alpha^{\circ}}{360^{\circ}} \therefore A=\frac{\pi r^2 180^{\circ}} {360^{\circ}} \therefore A=\frac{\pi r^2}{2}\\ \\ \\ A=\frac{r^2 \beta }{2} \therefore A=\frac{r^2 \pi }{2} \therefore A=\frac{\pi r^2}{2}$

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.