# Areas of Sectors and Segments

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

Key stage:  KS 4

Curriculum topic:  Geometry and Measures

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

Difficulty level:

### 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

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

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

4.29
• Question 4

Calculate the area of the sector.

 Remember, area = x R2 x 360

R = 21 cm

θ = 48°

Area = ____ cm2

184.73
• Question 5

Calculate the area of the sector.

 Remember, area = x R2 x 360

R = 7.5 cm

θ = 35°

Area = ____ cm2

17.18
• Question 6

Calculate the area of the sector.

 Remember, area = x R2 x 360

R = 3.5 cm

θ = 21°

Area = ____ cm2

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

37.55
• Question 8

Calculate the area of the segment.

R = 21.5 cm

θ = 31°

Area = ____ cm2

6.01
• Question 9

Calculate the area of the segment.

R = 2.5 cm

θ = 22°

Area = ____ cm2

0.03
• Question 10

Calculate the area of the segment.

R = 10 cm

θ = 44°

Area = ____ cm2