Page 66 - Focus SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 1 Circular Measure

B Determining the area of segment of 13
a circle
Calculate the area, in cm , of the shaded segment for
2
1. Observe that the area of segment of a circle each of the following circles.
represented by the shaded region can be
determined by subtracting the area of triangle [Use π = 3.142]
from the area of sector of the circle. (a)
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2 rad
r p O 3.5 cm
θ
O
r

(b)
2. For a circle with radius r, the area of triangle can 60º
1
be determined by using the formula A = r sin 23 cm
2
2 O
1
q or A = s(s – p)(s – r) , such that s = (2r + p).
2
2
3. By using A = 1 r q and A = 1 r sin q or
2
2
2 2 Solution
A = s(s – p)(s – r) , the following formulae can 1 2
2
be derived to determine the area of segment of (a) A = r (q – sin q)
2
a circle. 1 2
(a) Area of segment of a circle = (3.5) (2 – sin 2)
2
= Area of sector – Area of triangle = 6.681 cm
2
1
= 1 r q – r sin q
2
2
2 2
1
= 1 r (q – sin q) (b) 60° = 60° × 3.142 2 rad
2
2 180°
= 1.047 rad
(b) Area of segment of a circle
1
= Area of sector – Area of triangle A = r (q – sin q)
2
2
= 1 r q – s(s – p)(s – r)
2
2
2 = 1 (23) (1.047 – sin 60°)
2
1
such that s = (2r + p) 2
2 = 47.87 cm
2
Form 5
REMEMBER! SPM Tips
Solution of triangles in circular measure can involve the If the angle θ is given in the unit of degrees, use it directly
use of two different types of formulae, which is to find the sine value. Converting degrees to radians will
1 only reduce the accuracy of the sine value.
A = ab sin C, or
2
A = s(s – a)(s – b)(s – c)
such that s = 1 (a + b + c)
2
Try Questions 6 - 7 in ‘Try This! 1.3’

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