Question

Find the area of each sector shown (the shaded section)

Answer 1

The area of the sector (shaded section) is 29.51
`m^(2)`.

Explanation:

Area of a sector = (θ ÷ 360)
`\pi`
`r^(2)`

where θ is the central angle of the sector, and r is the radius of the circle.

From the diagram give, diameter of the circle is 26 m. So that;

r =
`(diameter)/(2)`

=
`(26)/(2)` = 13 m

θ = 360 - (180 + 160)

= 360 - 340

=
`20^(o)`

Thus,

area of the given sector =
`(20)/(360)` x
`(22)/(7)` x
`(13)^(2)`

=
`(20)/(360)` x x
`(22)/(7)` x 169

= 29.5079

The area of the sector (shaded section) is 29.51
`m^(2)`.