Question

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

Answer 1

Answer:

3 m^2

Step-by-step explanation:

The shaded area = Area of Sector - Area of Triangle

First we find area of sector = $\frac{\theta}{360}*\pi r^2$

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

$\frac{\theta}{360}*\pi r^2\\\frac{60}{360}*\pi (6)^2\\=18.85$

Secondly, we find area of triangle (isosceles) = $\frac{1}{2}abSinC$

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:

$\frac{1}{2}(6)(6)Sin(60)\\=15.59$

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

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