# Worksheet: Area of a Circular Sector

In this worksheet, we will practice finding the area of a circular sector given the radius and the measure of the central angle.

**Q3: **

Find the area of the shaded part of the diagram in terms of .

- A
cm
^{2} - B
cm
^{2} - C
cm
^{2} - D
cm
^{2}

**Q5: **

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

**Q6: **

The radius of a circle is 12 cm and the angle of a sector is . Find the area of the sector giving the answer in terms of .

- A
cm
^{2} - B
cm
^{2} - C
cm
^{2} - D
cm
^{2}

**Q9: **

In this figure, the diameter of the larger circle is 41 cm and both circles have the same centre. Determine, to the nearest tenth, the area of the shaded part.

- A
280.2 cm
^{2} - B
412.8 cm
^{2} - C
617.6 cm
^{2} - D
696.2 cm
^{2} - E
1 788.8 cm
^{2}

**Q11: **

is a right-angled triangle at where and . The arc of a circle touches point and cuts at the point . Find the area of the part bounded by , and the arc giving the answer to one decimal place. Consider having a diagram.

**Q13: **

The area of a circular sector is 12 cm^{2} and the
perimeter is 16 cm. Find all possible values for the
radius.

- A 12 cm or 3 cm
- B 12 cm or 4 cm
- C 7 cm or 2 cm
- D 6 cm or 2 cm
- E 7 cm or 4 cm

**Q15: **

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 yards. 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 sq yards
- B sq yards
- C sq yards
- D square yards
- E sq yards

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 yards
- B yards
- C yards
- D yards
- E yards

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

- A sq yards
- B sq yards
- C sq yards
- D sq yards
- E sq yards

**Q16: **

is an equilateral triangle with a side length of 92 cm. Three circular sectors are drawn in the triangle such that their centres are the vertices , and . The radius of each sector is 46 cm. Find the area of the part of the triangle bounded by the arcs of the circular sectors giving the answer to one decimal place.