# A sector of a circle of radius 8cm has an angle of theta radians. The perimeter of the sector is 30cm?

Find the area of the sector

Relevance

Draw a circle.

Show

i) Sector containing angle theta, and label the radius 8

ii) Shade in the pie-shaped sector

Here's the logic:

This circle has Area=(pi)r^2

Area=(pi)8^2

Area=64(pi)

The sector's Perimeter is 30

Since the two arms of the sector are radii, and since each radii=8,

Length of sector's arc=30-(8+8)

Arc=30-16

Arc=14

Now, Circumference of the circle=(pi)d

C=(pi)2r

C=16(pi)

Therefore the ratio of the arc to the circumference= 14/16(pi), or 7/(8pi)

The area of the sector is thus 7/(8pi) of 64(pi)

7/(8pi) / 64pi

=7/8pi X 64pi/1

=7 X 8

=56 cm^2