Page 24 - Module & More Matematik Tambahan TG5

Matematik Tambahan Tingkatan 5 Bab 1 Sukatan Membulat
Sudut KBATKBAT KBAT

EKSTRA
1

Rajah di bawah menunjukkan sebuah bulatan (a) Cari sudut SOP dalam radian. BAB
berpusat O dan berjejari 10 cm. PQ dan SR adalah dua Find the angle of SOP in radians.
perentas yang selari dengan PQ = 10 cm dan ∠SOR = (b) Tentukan luas rantau berlorek itu.
120°. Determine the area of the shaded region.
The diagram below shows a circle with centre O and radius (c) Tunjukkan bahawa perimeter rantau berlorek ialah


10 cm. PQ and SR are two parallel chords such that PQ = 10 10 1 + 3 + π  cm.
cm and ∠SOR = 120°. KBAT Menganalisis 3
Show that the perimeter of the shaded region is

P Q 10 1 + 3 + π  cm.
S R 3
O

2
2
2
(a) PQ = 10 + 10 − 2(10) kos POQ Luas tembereng SR / Area of segment SR
2
1
2
2
10 + 10 − 10 2 = 1 (10) 2  2π  − (10) sin 120°
2
kos POQ = 2 3 2
2(100)
∠POQ = 60° = 61.42 cm 2
120°−60° Maka, luas berlorek
∠SOP = 1 Penerbitan Pelangi Sdn. Bhd.
Hence, the shaded area

2
π = 61.42 – 9.06
= 30° = rad = 52.36 cm 2
6
10 cm (c) Panjang lengkok SP = QR
P Q Arc length SP = QR
S R
π
120 10   = 5π
10 cm 6 3
O
2
2
2
SR = 10 + 10 − 2(10) kos 120°
2
SR = 10 3
5π
(b) Luas tembereng PQ /Area of segment PQ Perimeter = 10 + 2   + 10 3
1 π 3
= (10) 2   − (10) sin 60° π
2

2 3 2 = 10 1+ + 3 
= 9.06 cm 2 3

Jawapan
Enrolment key Bab 1
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01 M&M Mate T Tg5.indd 21 09/12/2022 12:21 PM