The area of a shape is the amount of space on the shape.
The area of the shaded region is 819 inches square
How to determine the area of the shaded region
Start by calculating the area of the sector using:
[tex]A = \frac{\theta}{360}*\pi r^2[/tex]
So, we have:
[tex]A = \frac{150}{360}*\frac{22}{7} * 27.8^2[/tex]
[tex]A = 1012.05[/tex]
Next, calculate the area of the isosceles triangle using:
[tex]A = \frac 12 r^2\sin(\theta)[/tex]
So, we have:
[tex]A = \frac 12 * 27.8^2 * \sin(150)[/tex]
[tex]A = 193.21[/tex]
The shaded area is the difference between the areas of the sector and the triangle.
So, we have:
[tex]A = 1012.05 - 193.21[/tex]
Calculate the difference
[tex]A = 818.84[/tex]
Approximate
[tex]A = 819[/tex]
Hence, the area of the shaded region is 819 inches square
Read more about areas at:
https://brainly.com/question/10090807
