Name: Natashia
Who is asking: Student
Level of the question: Middle

Question: How do you find the area of a shaded sector of a circle?

 


Natashia,

The area of the sector depends on the radius of the circle r and the measure of the angle t.

If the measure of the angle is 360o the the sector is the entire circle and the area is r2

area = r2

If the measure of the angle is 180o the the sector is one half the circle and the area is 1/2 r2

area = 1/2 r2

If the measure of the angle is 90o the the sector is one quarter the circle and the area is 1/4 r2

area = 1/4 r2

If the measure of the angle is 45o the the sector is one eighth the circle and the area is 1/8 r2

area = 1/8 r2

What you can see is that the area of the sector is a fraction of the area of the circle , and the fraction is the same fraction that the angle is of 360o. Thus if the radius of the circle is r and the central angle of the sector has measure t then

the area of the sector is t/360  r2.

Penny