Question

estion 14 (2 points)nd the area of the Segment of a circle (the shaded part). Round your answer to the nearest tenth.BсDadius is 5 ft and the Central angle (m

Answer 1

Given the shown figure

radius= 5ft

m

First solve the portion of the circle

`Pc=(\theta)/(360)*\pi *r^2`
`Pc=(74)/(360)*\pi *5^2`
`Pc=(185\pi)/(36)=16.14`

Now solve the area of the inner triangle

`At=(1)/(2)a*b*sin(\theta)`
`At=(1)/(2)*5*5*sin(74)`
`At=12.015`

then the area of the shaded region is

`A=Pc-At`
`A=16.14-12.015`
`A=4.1285ft^2`

Area of the shaded part is 4.1285ft^2