Page 13 - Matematik Tam_Modul A+_Pan Asia Publications

(c) (d)
P
B
6.5 cm
O
O
5 cm
30°
A
Q ∠AOB π
∠POQ = 180° – 60° = 120° 3 = rad SP 1.3.2 & 1.3.3
3
120° × π = 2π rad Luas rantau berlorek
( )
180° 3 = 3 [ 1 (5) 2 π – (5) sin π × 180° 2]
1
2
Luas rantau berlorek 2 3 2 1 3 π
©PAN ASIA PUBLICATIONS
( )
1
1
= (6.5) 2 2π – (6.5) sin 120° = 6.79 cm 2
2
2 3 2
= 25.95 cm 2

Uji Kendiri 1.3

1. Rajah menunjukkan sebuah kipas tangan berbentuk 2. Rajah menunjukkan dua sektor bulatan, OACB dan
sebuah sektor dan bahagian berlabel ABCD yang CBOA, masing-masing dengan pusat O dan C.
diperbuat daripada kain. The diagram shows two sectors, OACB and CBOA, with centres
The diagram shows a fan in a form of a sector and the area O and C respectively.
labelled ABCD is made of cloth. B
13 cm B C
14 cm A kain M O
θ cloth
A
Diberi bahawa OC adalah berserenjang dengan AB dan
D
C melalui titik tengah M. Jika OB = 8 cm,
Given that OC is perpendicular to AB and passes through the
)
Diberi perimeter kain ialah ( 41 + 26 cm, cari midpoint M. If OB = 8 cm, 2
4π
(a) buktikan bahawa sudut AOB ialah π,
)
2
Given the perimeter of the cloth is ( 41 + 26 cm, find show that the angle AOB is π, 3
4π
(a) sudut q, 3
the angle q, (b) cari luas rantau berlorek itu.
(b) luas kain itu dalam sebutan π. find the area of the shaded region.
the area of the cloth used in terms of π. KBAT Menganalisis
KBAT Mengaplikasi (a) OB = 8 cm, OM = 4 cm
4
8
(a) 14q + 27q = 41 + 26 – 26 kos MOB = = 1
2
4π ∠MOB = 60°
41q = 41 π 120° 2
4 ∠AOB = 360° × 2π = π rad
3
1
( )
q = π rad 1 2 2
4 (b) Luas sektor AOB = (8) 3 π
2
(b) Luas kain = 67.02 cm 2
( )
( )
1
1
1
= (27) 2 1 π – (14) 2 1 π Luas ∆OAB = (8) sin 120°
2
2 4 4 4 2
1
1
= 91 π – 24 π = 27.71 cm 2
2 2 Luas rantau berlorek = 67.02 – 27.71
5
= 66 π cm 2 = 39.31 cm 2
8
( )
1
Luas sektor ACB = 2 [ 1 (8) 2 π – (8) sin 60°]
2
3
2
2
= 11.60 cm 2
Luas rantau berlorek = 39.31 + 11.60
= 50.91 cm 2
11
01 ModulA+ MateTambahan Tg5.indd 11 10/30/20 10:02 AM