Question

Find the area of the shaded segment. Round your answer than your square meter.

Answer options: 3m2, 5m2, 6m2, 4m2.

Answer 1

3 m^2

Explanation:

The shaded area = Area of Sector - Area of Triangle

First we find area of sector =
`(\theta)/(360)*\pi r^2`

We know the angle is 60° (vertical angles are equal) and the radius is 6, so we find the area of sector to be:

`(\theta)/(360)*\pi r^2\\(60)/(360)*\pi (6)^2\\=18.85`

Secondly, we find area of triangle (isosceles) =
`(1)/(2)abSinC`

where

a and b are the two sides bordering the known angle, so a=b=6, and

C is the angle which is 60°

Now we find the area to be:

`(1)/(2)(6)(6)Sin(60)\\=15.59`

Hence, area of shaded =
`18.85 - 15.59=3.26`

Rounding to nearest whole number, area of shaded region = 3m^2