This presentation shows worked examples of finding the perimeter of a sector of a circle.

1. PERIMETER OF A
SECTOR

2. Sector of a Circle
The sector of a circle is a part of the circle made
up of an arc along with two radii which are at the
end points of the arc.
The diagram shows a circle divided into two
sectors; a major sector and a minor sector.

3. Perimeter of a sector of a circle
RECALL:
Perimeter is the distance around a figure.
The perimeter of a sector would be the sum of
the length of the arc, and the two radii.
𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 𝑠𝑒𝑐𝑡𝑜𝑟 = 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑎𝑟𝑐 + 𝑟𝑎𝑑𝑖𝑢𝑠 + 𝑟𝑎𝑑𝑖𝑢𝑠

4. RECALL: Length of an Arc

5. EXAMPLE: Use 𝜋 =
22
7
.
Calculate the perimeter:
𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 = 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑎𝑟𝑐 + (2 × 𝑟𝑎𝑑𝑖𝑢𝑠)
=
64
360
× 2 ×
22
7
× 5.5 + (2 × 5.5)
= 𝟏𝟕. 𝟏 𝒎
Calculate the perimeter:
𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 = 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓𝑎𝑟𝑐 + (2 × 𝑟𝑎𝑑𝑖𝑢𝑠)
=
197
360
× 2 ×
22
7
× 7.7 + (2 × 7.7)
= 𝟒𝟏. 𝟗 𝒎𝒎

6. EXAMPLE: Use 𝜋 =
22
7
.
Calculate the perimeter:
𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 = 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑎𝑟𝑐 + (2 × 𝑟𝑎𝑑𝑖𝑢𝑠)
=
284
360
× 2 ×
22
7
× 3.6 + (2 × 3.6)
= 𝟐𝟓 𝒎𝒎
Calculate the perimeter:
𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 = 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓𝑎𝑟𝑐 + (2 × 𝑟𝑎𝑑𝑖𝑢𝑠)
=
126
360
× 2 ×
22
7
× 4.8 + (2 × 4.8)
= 𝟐𝟎. 𝟐 𝒄𝒎

7. EXAMPLE: Use 𝜋 =
22
7
.
Calculate the perimeter:
𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 = 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑎𝑟𝑐 + (2 × 𝑟𝑎𝑑𝑖𝑢𝑠)
=
275
360
× 2 ×
22
7
× 9 + (2 × 9)
= 𝟔𝟏. 𝟐 𝒄𝒎
Calculate the perimeter:
𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 = 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓𝑎𝑟𝑐 + (2 × 𝑟𝑎𝑑𝑖𝑢𝑠)
=
249
360
× 2 ×
22
7
× 9.2 + (2 × 9.2)
= 𝟓𝟖. 𝟒 𝒎

8. Example
 Perimeter of plot = 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑎𝑟𝑐 + 𝑟𝑎𝑑𝑖𝑢𝑠 + 𝑟𝑎𝑑𝑖𝑢𝑠
=
60
360
× 2 ×
22
7
× 28 + 28 + 28
` = 85.3 𝑚
A plot of land is in the shape of a sector of a circle of radius 28 m.
If the sectorial angle (central angle) is 60°, find the perimeter of the plot.
(𝑈𝑠𝑒 𝜋 =
22
7
. )

9. Example
 Perimeter of plot = 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑎𝑟𝑐 + 𝑟𝑎𝑑𝑖𝑢𝑠 + 𝑟𝑎𝑑𝑖𝑢𝑠
30 = 16 + 2𝑟
` 2𝑟 = 30 − 16 = 14
𝑟 = 7 𝑐𝑚
Find the radius of sector whose perimeter is 30 cm and length of the arc
is 16 cm.

10. Example
 Perimeter of plot = 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑎𝑟𝑐 + 𝑟𝑎𝑑𝑖𝑢𝑠 + 𝑟𝑎𝑑𝑖𝑢𝑠
45 = 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑎𝑟𝑐 + 10 + 10
45 = 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑎𝑟𝑐 + 20
𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑎𝑟𝑐 = 45 − 20
= 25 𝑐𝑚
Find the length of arc, if the perimeter of the sector is 45 cm and the
radius is 10 cm.

11. THE END.