What is the area of the shaded region below?

Question

anonymous · Answer

attachment

anonymous · Answer

I know the total area is 201.06.

mathstudent55 · Answer

The area of a sector of a circle is

$A = \dfrac{n}{360^o}\pi r^2$

where A = area of sector
n = central angle that intercepts the sector (in degrees)
r = radius of circle

mathstudent55 · Answer

You are correct about the total area of the circle.
The fraction in the beginning of the formula for the area is simply taking care of the fraction of the area of the entire circle that the sector is.

A full circle corresponds to a central angle of 360 degrees.
A central angle of n degrees intercepts a sector whose area is n/360 times the area of the circle.

anonymous · Answer

So the final answer would be 86.52 units?

mathstudent55 · Answer

$A = \dfrac{155^o}{360^o} \times 201.06$

You are correct.

anonymous · Answer

Thank you for breaking it down. I appreciate it.

mathstudent55 · Answer

You are welcome.