Page 14 - Modul A+1 Matematik Tambahan Tingkatan 5

(c) (d)
P
B
6.5 cm
O
O
C
5 cm
30° BAB 1
A
D
Q
π
∠POQ = 180° – 60° = 120° ∠BOC = ∠AOB = rad
3
3
120° × π = 2π rad Luas tembereng
180° 3
( )
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1
2
Luas tembereng = 3 [ 1 (5) 2 π – (5) sin 1 π × 180° 2]
2
π
3
2
3
( )
1
1
= (6.5) 2 2π – (6.5) sin 120° 2
2
2 3 2 = 6.79 cm
= 25.95 cm 2
Uji Kendiri 1.3
1. Rajah menunjukkan sebuah kipas tangan berbentuk 2. Rajah menunjukkan dua sektor bulatan, OACB dan
sektor OABCD dan bahagian berlabel ABCD diperbuat CBOA, masing-masing dengan pusat O dan C.
daripada kain. The diagram shows two sectors, OACB and CBOA, with centres
The diagram shows a hand fan in a form of a sector OABCD O and C respectively. KBAT Mengaplikasi
and the area labelled ABCD is made of cloth. B
KBAT Mengaplikasi
C

B M
13 cm O
A
14 cm Kain A
Cloth
O θ Diberi bahawa OC adalah berserenjang dengan AB dan
D melalui titik tengah M. Jika OB = 8 cm,
C
Given that OC is perpendicular to AB and passes through the
midpoint M. If OB = 8 cm,
)
2
Diberi perimeter kain ialah ( 41 p + 26 cm, cari (a) tunjukkan bahawa sudut AOB ialah π,
3
4
2
)
3
Given the perimeter of the cloth is ( 41 p + 26 cm, find show that the angle AOB is π,
4
(a) nilai q, dalam radian, (b) cari luas kawasan berlorek itu.
the value of q, in radians, find the area of the shaded region.
(b) luas kain itu, dalam sebutan π. (a) OB = 8 cm, OM = 4 cm
the area of the cloth, in terms of π.
4
kos ∠MOB =
8
∠MOB = 60°
(a) 14q + 27q = 41 p + 26 – 26 p 2
4 ∠AOB = 120° × 180° = π rad
3
( )
41q = 41 π 1 2 2
4 (b) Luas sektor AOB = (8) 3 π
2
1
q = π rad = 67.02 cm 2
4 1
2
(b) Luas kain Luas ∆OAB = (8) sin 120°
2
( )
( )
1
= (27) 2 1 π – (14) 2 1 π = 27.71 cm 2
2 4 2 4 Luas kawasan berlorek = 67.02 – 27.71
1
1
= 91 π – 24 π = 39.31 cm 2
8 2 1 2 π 1
5
2
3
2
= 66 π cm 2 Luas sektor ACB = 2 [ 2 (8) ( ) – (8) sin 60° ]
8
= 11.60 cm 2
Luas kawasan berlorek = 39.31 + 11.60
= 50.91 cm 2
11
01 Modul Series MateTam Tg5.indd 11 04/10/2021 2:15 PM