Area of Sector Discovery

Area of Sectors

​How do you find the area of a sector of a circle?

What is a SECTOR?

A sector of a circle is a region bounded by two radii and their intercepted arc.

A sector is named by the endpoints of the arc and the center of the circle. For example, the figure shows sector POQ.

Let's derive the formula for the area of a sector

The following questions will walk you through "discovering" the formula for finding the area of a sector in a circle.

Multiple Choice

Which of the following is the formula for finding area of a circle?

• $$A=\pi r^2$$

• $$A=3r^2$$

• $$A=0.5\pi r^2$$

• $$A=2\pi r$$

Dropdown

First, find the area of the circle.



$$A=\pi r^2$$ = π(​​

Select answer

)²



A ≈ ​​

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Dropdown

The area of sector AOB is $$\frac{1}{3}$$ of the circle's area.



Area of sector AOB = $$\frac{1}{3}$$ ∙ ​

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= ​

Select answer

mm²

Open Ended

How could you use the above process to find the area of a sector of the circle whose central angle

measures m°?

Multiple Choice

What do you think is the formula for the area of a sector with a central angle of x° and radius r?

• $$\frac{x\cdot2\pi r}{180}$$

• $$\frac{x\cdot\pi r^2}{360}$$

• $$\frac{x\cdot2\pi r}{360}$$

• $$\frac{x\cdot\pi r^2}{180}$$

​Area of a Sector

Labeling

Find the area of the sector, round the nearest hundredth.

$$A=\frac{x\degree\cdot\pi r^2}{360}$$

Drag labels to their correct position on the image

11

6

3

16.49

360

9

150

0.58

48.47

210

Labeling

Find the area of the sector, round the nearest hundredth.

Drag labels to their correct position on the image

27.43

287.77

47.96

144

24

164.62

131

229

360

12

Open Ended

Your friend said that the value of x° in the formula for the area of a sector can never be larger than 360°. Do you agree or disagree? Explain your reasoning.

Math Response

Find the area of the sector, round to the nearest hundredth.

Type answer here

Correct Answer: 1

Deg^°

Rad

Math Response

Find the area of the sector, round to the nearest hundredth.

Type answer here

Correct Answer: 113.1

Deg^°

Rad