# Lesson Worksheet: Areas of Circular Sectors Mathematics

In this worksheet, we will practice finding the area of a circular sector and solving problems that relate this area to the arc length and perimeter of the sector.

**Q1: **

Write an expression for the area of a sector whose arcβs measure is radians, knowing that the expression for the area of a sector measuring degrees is .

- A
- B
- C
- D
- E

**Q2: **

Work out the area of the given shape, giving your answer accurate to two decimal places.

**Q3: **

The radius of a circle is 21 cm and the angle of a sector is . Find the area of the sector giving the answer to the nearest square centimeter.

**Q4: **

An arc has a measure of radians and a radius of 5. Give the area of the sector, in terms of , in its simplest form.

- A
- B
- C
- D
- E

**Q5: **

Find the area of the colored part of the diagram, giving the answer to one decimal place.

**Q6: **

The area of a circular sector is of the area of a circle, find, in radians, the central angle, correct to one decimal place.

**Q7: **

Given that the area of the colored part in the figure is 155 cm^{2}, find the value of to the nearest tenth.

**Q8: **

A landscape gardener decides that he wants to design a lawn split into a series of sectors with circular patios laid into the grass, as shown in the given figure. The circular lawn will be split into six equal sectors, each with a radius of eight meters. The lines and are both tangents to the circle, and the arc touches the circle at a single point.

Work out the area of sector . Give your answer in terms of .

- A square meters
- B square meters
- C square meters
- D square meters
- E square meters

The gardener needs to calculate the radius of the circular patio. Using trigonometric ratios, calculate the radius of the patio. Give your answer as a fraction.

- A meters
- B meters
- C meters
- D meters
- E meters

Calculate the total area of grass in one sector. Give your answer, in terms of , in its simplest form.

- A square meters
- B square meters
- C square meters
- D square meters
- E square meters

**Q9: **

Three congruent circles with a radius of 43 cm are placed touching each other. Find the area of the part between the circles giving the answer to the nearest square centimeter.

**Q10: **

The radius of a circle is 10 cm and the perimeter of a sector is 25 cm. Find the area of the sector.