Page 11 - Matematik Tam_Modul A+_Pan Asia Publications

2. Hitung jejari j dan/atau sudut q dalam radian bagi setiap yang berikut.
Calculate the radius j and/or the angle q in radians for each of the following. TP 3
(a)
Contoh/Example Luas rantau berlorek
Luas rantau berlorek
7 cm Area of shaded region
Area of shaded region = 20 cm 2
θ = 24 cm 2 1.3 rad q = 1.3 rad
Jejari/Radius = 7 cm
j
SP 1.3.1

Luas / Area = j q 1
1 2
2 2 (1.3)j = 20
2
1
2
24 = (7) q j = 20 × 2
2
2 1.3
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q = 48 j = 5.55 cm
49
= 0.98 rad

(b) (c)
Jejari/Radius = 10 cm 10 cm Luas rantau berlorek
Luas rantau berlorek Area of shaded region
Area of shaded region = 30 cm 2
O = 100 cm 2 j Panjang lengkok
10 cm θ θ Length of arc
= 10 cm

1
j q = 30 .................a
2
2
100 = (10) (2π – q) 1 2
2 jq = 10 .................b
2 = 2π – q 1
q = 2π – 2 a ÷ b 2 j = 3
= 4.28 rad j = 6 cm
ºq = 10
6
= 5 rad
3

3. Hitung luas bagi setiap rantau berlorek yang berikut.
Calculate the shaded area for each of the following. TP 4

(a)
Contoh/Example P OR = RQ = 2.3 cm
O OA = OD = 5 cm
AB = CD = 3 cm S 1.4 rad Q
1.6 rad D R
A C O

B
1
Luas / Area OBC = (8) (1.6)
2
2
1
Luas / Area OAD = (5) (1.6) Luas rantau berlorek
2
2
1
1
2
2
Luas rantau berlorek/Area of shaded region = (4.6) (2π – 1.4) – (2.3) (2π – 1.4)
2
2
1
1
= (8) (1.6) – (5) (1.6) = 38.75 cm 2
2
2
2 2
= 31.2 cm 2
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