Page 16 - PBD Plus Matematik Tambahan T5 (EG)

Matematik Tambahan Tingkatan 5 Bab 1 Sukatan Membulat

(b) Diberi POQ dan SOR P (c)
adalah dua sektor dengan T P
pusat O dan /POQ = 2SOR 3 cm
= 1.3 rad. Cari jumlah luas O Q O A
rantau berlorek. S
Given that POQ and SOR are two U Q
sectors with centre O and /POQ = R Diberi /PAQ = 45° dan PA = 6 cm dan OP = 5 cm.
2SOR = 1.3 rad. Find the total area
of shaded region. Cari luas rantau berlorek.
Given /PAQ = 45° and PA = 6 cm and OP = 5 cm. Find the area
1
Luas sektor POQ = j q = (3) (1.3) of shaded region.
2
1 2
Area of sector POQ 2 2
= 5.85 cm 2 Perentas PQ = √
6 + 6 – 2(6) kos 45°
2
2
2
1.3 rad = 1.3 × 360° = 74.48° Chord PQ = 4.59 cm
2π 2 2 2
1
Luas segi tiga POQ = (3) sin 74.48° kos/cos /POQ = 5 + 5 – 4.59
2
2
2(5)
Area of triangle POQ 2
= 4.34 cm 2 /POQ = 54.65°
= 0.954 rad
Maka, luas tembereng PTQ = 5.85 – 4.34
Hence, area of segment PTQ = 1.51cm 2 Luas rantau berlorek
Area of shaded region
1
 2
Luas sektor SOR = j q = ( 3) 2 1.3 1 2 1 2 1 2
1 2
2
2
Area of sector SOR 2 2 2 = 2 (6) (0.785) – (6 )sin 45° + (5 )(0.954)
= 2.93 cm 2 – ( 5) sin 54.65°
1
2
1.3 rad = 0.65 × 360° = 37.24° 2
2 2p 2Pelangi Sdn. Bhd.
= 3.13 cm
2

1
Luas segi tiga SOR = (3) sin 37.24°
2
Area of triangle SOR 2
= 2.72 cm 2
Maka, luas tembereng SUR = 2.93 – 2.72
Hence, area of segment SUR = 0.21cm 2
Penerbitan
Jumlah luas rantau berlorek = 1.51 + 0.21
Total area of the shaded region = 1.72 cm

Cuba jawab Praktis SPM 1, K1: S2

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