1. SECTORS A sector is basically a “slice”.x°
The area of a sector is proportional to the size of the angle at the middle, x°.
Ex1
90° is quarter of a full turn
sector
Sector area = 400cm2  4 = 100cm2
Area = 400cm2

2. For more difficult angles we can cross-multiply as follows….
Ex2
Angle = sector
sector
area circ
45°
= sector
360 X sector = 45 X 56
Area circle = 56m2
sector =  360
sector = 7m2

3. Ex3 Angle = sector 360 area circ 108 = sector 360 314
10cm
108°
area circ
= sector
r = 10
360 X sector = 108 X 314
A = r2
sector =  360
= 3.14 X 10 X 10
= 314
sector = cm2

4. Ex4 Angle = sector 360 area circ 216 = sector 360 706.5
15m
Angle = sector
144°
area circ
sector
= sector
r = 15
360 X sector = 216 X 706.5
A = r2
sector =  360
= X 15 X 15
sector = =
arc = 424m2 ( 3 sfs)
Sector angle = 360° - 144°
= 216°

5. Ex5
A slice of pizza has a radius of 18cm. The angle in the centre is 40° What is its area?
40°
18cm
***********
r = 18
Angle = sector
area circ
A = r2
= sector
= 3.14 X 18 X 18 =
360 X sector = 40 X
sector =  360 =
= 113cm2

6. Work for this is on pages 41-43, Ex2