Page 36 - Hybrid PBD 2022 Tg 5 - Matematik Tambahan

Matematik Tambahan Tingkatan 5 Bab 1 Sukatan Membulat
(b) perimeter rantau berlorek. (b) panjang perentas AB
the perimeter of the shaded region. length of chord of AB
[2 markah / 2 marks] = √
9 + 9 – 2(9) kos 120°
2
2
2
Tip KBATKBAT = 15.59 cm
KBAT
Gunakan petua sinus. 2p
Using sine rule. panjang lengkok = 9  2 = 6π
arc length 3
\ Perimeter bahagian berlorek = 15.59 + 6π
Jawapan / Answer :
Perimeter of the shaded region = 34.44 cm 2
(a) 0.75 rad B
0.75
= × 360° Kertas 2
2π 0.75 rad
= 42.97°
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O 4 cm C A 1. Rajah menunjukkan dua sektor,
/OCB = 94.06° OAB berpusat O dan BAC berpusat B A
OB 4 A.
sin 94.06° = sin 42.97° The diagram shows two sectors, OAB with
OB = 5.85 cm centre O and BAC with centre A. C
Diberi OA = 18 cm dan AB = 12 O
(b) panjang lengkok = 5.85 (0.75) cm, cari
arc length = 4.39 cm Given OA = 18 cm and AB = 12 cm, find
(a) /BAC dalam radian.
Perimeter rantau berlorek = 4 + 4.39 + (5.85 – 4) /BAC in radians.
Perimeter of the shaded region = 10.24 cm [2 markah / 2 marks]
(b) perimeter rantau berlorek.
the perimeter of the shaded region.
4. Rajah menunjukkan sebuah bulatan berpusat O [4 markah / 4 marks]
dan berjejari 9 cm. KBAT Mengaplikasi (c) luas rantau berlorek itu.
The diagram shows a circle with centre O and a radius of 9 cm. the area of the shaded region.
[4 markah / 4 marks]
C
Jawapan / Answer :
A B
(a) OA = 18 cm
O 6
kos/cos ∠BAC =
18
AOB ialah suatu lengkok bagi satu bulatan ∠BAC = 70.53
berpusat C yang terletak pada lilitan bulatan. Cari. = 1.23 rad
AOB is an arc of a circle with centre C which is on the
circumference of the circle. Find (b) panjang lengkok BC = 12(1.23)
(a) /AOB, dalam radian arc length = 14.77 cm
/AOB, in radians. /BOA = 180° – 2(70.53°)
[2 markah / 2 marks] = 38.94°
(b) perimeter bahagian berlorek. = 0.68 rad
the perimeter of the shaded region. panjang lengkok BA = 18(0.68)
[3 markah / 3 marks] arc length = 12.23 cm

Tip KBATKBAT Perimeter rantau berlorek = 12.23 + 14.77 + 12
KBAT
Perhatikan CO berserenjang dengan AB dan Perimeter of the shaded region = 39 cm
AOBC ialah sebuah rombus. Gunakan petua 1 2
kosinus untuk mencari panjang perentas. (c) Luas sektor BAC = (12) 1.23
2
It is observed that CO is perpendicular with AB Area of sector of BAC
and AOBC is a rhombus. Use cosine rule to find the = 88.56 cm 2
length of chord. Luas tembereng BAD
Area of segment of BAD
Jawapan / Answer : 1 1
= (18 )(0.68) – (18) sin 38.94°
2
2
(a) AO = OB = CA = CB = CO 2 2
A B = 8.34 cm 2
Maka ∠AOC = 60° =∠COB θ 9
O Jumlah luas rantau berlorek
q = 120° = 2π rad Total area of the shaded region
3
= 8.34 + 88.56
= 96.9 cm 2
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01 Hybrid PBD Mate Tamb Tg5.indd 15 09/11/2021 9:20 AM