Question

URGENT Find the area of the shaded region.​

Answer 1

Answer: 3.32276 units squared

Explanation:

area of total sector=(pi*r^2)/360

=2^2 * 120pi /360

=4*120/360 * pi

=4.1887902

area of the triangle=(1/2)*base*height

the height is 1 (because you can divide the triangle down the middle to make a 30 60 90 triangle, and the sin(30)=x/2, so 2sin(30)=x, x=(1/2)*2

the base is equal to
`√(3)` because the base of the 30 60 90 triangle is 2sin(60), and sin60 is
`√(3)`/2, so you have to double that to get the area of the 120 degree triangle.

the area of the triangle is (1/2)*1*
`√(3)`=
`√(3) /2`=0.866025

so the difference is 4.1887902-0.866025

=3.32276 units squared