Question

Please help!!!!!!!!!!

Answer 1

Suppose a sector of a circle with radius
`r` has a central angle of
`\theta`. Since a sector is a fraction of a full circle, the ratio of a sector's area A to the circle's area is equal to the ratio of a central angle to the measure of a full rotation of the circle. A full rotation of a circle is
`2\pi` radians. This proportion can be written as
`\boxed{(A)/(\pi r^(2))=(\theta)/(2\pi)}`. Multiply both sides by
`\pi r^2` and simplify to get
`\boxed{A=(\theta)/(2) r^(2)}`, where
`\theta` is the central angle of the sector and r is the radius of the circle.