Page 11 - Modul A+1 Matematik Tambahan Tingkatan 5

Uji Kendiri 1.2

1. Rajah menunjukkan sebuah sektor AOB berpusat O dan 2. Rajah menunjukkan sebuah semibulatan berpusat O
berjejari 8 cm. dan sebuah sektor APB dengan pusat P yang berjejari
The diagram shows a sector AOB with centre O and a radius 10 cm.
The diagram shows a semicircle with centre O and a sector APB
BAB 1 of 8 cm. KBAT Mengaplikasi with centre P and a radius of 10 cm. KBAT Mengaplikasi
A

12 cm
8 cm
B
θ A O
O 1.4 rad 10 cm
B
P
Diberi panjang lengkok AB ialah 12 cm, cari
Given the length of arc AB is 12 cm, find Cari
Find
(a) nilai q, dalam radian,
the value of q, in radians, (a) jejari semibulatan itu,
(b) panjang perentas AB. the radius of the semicircle,
the length of the chord AB. (b) perimeter kawasan berlorek itu.
the perimeter of the shaded region.
(a) 8q = 12 (a) 1.4 rad = 1.4 × 180°
q = 12 π
8 = 80.21°
= 1.5 rad
(b) 1.5 rad = 1.5 × 180° sin ( 80.21° ) = OB
2
10
π
= 85.94° OB = 6.44 cm
Panjang perentas AB (b) Perimeter = 6.44π + 10(1.4)
= ! 8 + 8 – 2(8) kos 85.94° = 34.23 cm
2
2
2
= ! 118.937
= 10.91 cm
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1.3 Luas Sektor Suatu Bulatan Buku Teks
Area of Sector of a Circle m.s. 12-19

1. Hitung luas kawasan berlorek yang berikut berdasarkan syarat-syarat yang diberi.
Calculate the area of the following shaded regions based on the given conditions. TP 3

Contoh/Example (a)
Luas
Gunakan/Use = 1 (3.5) (2.2)
2
1.4 = Luas/Area 3.5 cm 2
2π πj 2 O = 13.48 cm 2
10 cm 2.2 rad
O B Luas/Area
1.4 rad 1.4
= (10) 2
2
= 70 cm 2
A
(b) (c) 4.5 cm O
7.2 cm θ q = π
3θ 4
0.4 rad 3q = 3π
4
Luas Luas
( )
= 1 (7.2) (0.4) 1 2 3π
2
2 = 2 (4.5) 4
= 10.37 cm 2
= 23.86 cm 2

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