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Areas of Sectors and Segments

In this worksheet, students calculate the areas of sectors and segments.

'Areas of Sectors and Segments' worksheet

Key stage:  KS 4

Curriculum topic:  Geometry and Measures

Curriculum subtopic:  Calculate Arc Lengths, Angles and Areas of Sectors of Circles

Difficulty level:  

down

Worksheet Overview

QUESTION 1 of 10

Remember the following formulae:

Area of sector =  x r2 x /360

Area of triangle = ½ a b  sinC


We use these formulae to find the area of a segment.

 

Example

If R = 20 cm and   = 60º,

the area of the sector =  x 20 x 20 x 60 ÷ 360 = 209.44

the area of the triangle = ½ x 20 x 20 x sin 60º = 173.21

 

So the area of the segment = 209.44 - 173.21 = 36.23 cm2

Give all answers to 2 decimal places in this worksheet.

Calculate the area of the sector.

Remember, area = x R2 x
360

R = 10 cm

θ = 39°

Area = ____ cm2

 

Calculate the area of the segment.


Hint. Find the area of the sector, then the area of the triangle and subtract.

Use ½ab sin C to find the triangle's area.


 

R = 10 cm

θ = 72°

Area = ____ cm2

Calculate the area of the segment.


Hint. Find the area of the sector, then the area of the triangle and subtract.

Use ½ab sin C to find the triangle's area.

 

R = 12 cm

θ = 41°

Area = ____ cm2

Calculate the area of the sector.

Remember, area = x R2 x
360

R = 21 cm

θ = 48°

Area = ____ cm2

Calculate the area of the sector.

Remember, area = x R2 x
360

R = 7.5 cm

θ = 35°

Area = ____ cm2

Calculate the area of the sector.

Remember, area = x R2 x
360

R = 3.5 cm

θ = 21°

Area = ____ cm2

 

Calculate the area of the segment.

 

 

Hint. Find the area of the sector, then the area of the triangle and subtract.

Use ½ab sin C to find the triangle's area.

 

 

R = 14 cm

θ = 78°

Area = ____ cm2

 

Calculate the area of the segment.


 

R = 21.5 cm

θ = 31°

Area = ____ cm2

 

Calculate the area of the segment.



R = 2.5 cm

θ = 22°

Area = ____ cm2

 

Calculate the area of the segment.


 

R = 10 cm

θ = 44°

Area = ____ cm2

  • Question 1

Calculate the area of the sector.

Remember, area = x R2 x
360

R = 10 cm

θ = 39°

Area = ____ cm2

CORRECT ANSWER
34.03
  • Question 2

 

Calculate the area of the segment.


Hint. Find the area of the sector, then the area of the triangle and subtract.

Use ½ab sin C to find the triangle's area.


 

R = 10 cm

θ = 72°

Area = ____ cm2

CORRECT ANSWER
15.28
  • Question 3

Calculate the area of the segment.


Hint. Find the area of the sector, then the area of the triangle and subtract.

Use ½ab sin C to find the triangle's area.

 

R = 12 cm

θ = 41°

Area = ____ cm2

CORRECT ANSWER
4.29
  • Question 4

Calculate the area of the sector.

Remember, area = x R2 x
360

R = 21 cm

θ = 48°

Area = ____ cm2

CORRECT ANSWER
184.73
  • Question 5

Calculate the area of the sector.

Remember, area = x R2 x
360

R = 7.5 cm

θ = 35°

Area = ____ cm2

CORRECT ANSWER
17.18
  • Question 6

Calculate the area of the sector.

Remember, area = x R2 x
360

R = 3.5 cm

θ = 21°

Area = ____ cm2

CORRECT ANSWER
2.24
  • Question 7

 

Calculate the area of the segment.

 

 

Hint. Find the area of the sector, then the area of the triangle and subtract.

Use ½ab sin C to find the triangle's area.

 

 

R = 14 cm

θ = 78°

Area = ____ cm2

CORRECT ANSWER
37.55
  • Question 8

 

Calculate the area of the segment.


 

R = 21.5 cm

θ = 31°

Area = ____ cm2

CORRECT ANSWER
6.01
  • Question 9

 

Calculate the area of the segment.



R = 2.5 cm

θ = 22°

Area = ____ cm2

CORRECT ANSWER
0.03
  • Question 10

 

Calculate the area of the segment.


 

R = 10 cm

θ = 44°

Area = ____ cm2

CORRECT ANSWER
3.66
---- OR ----

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