Page 9 - Modul A+1 Matematik Tambahan Tingkatan 5

(b) S (c)
Q
P

O 1.5 rad θ
1.5 rad
BAB 1 j R O j P

Q Perimeter rantau berlorek = 16π + 24
Perimeter of the shaded region = 16π + 24
R OP = OQ = QP
OR = 2OP π
Perimeter rantau berlorek = 21 cm º q = 60° = 3
©PAN ASIA PUBLICATIONS
π
π
2
Perimeter of the shaded region = 21 cm j + πj + j + j + j = 16π + 24
2j + 2j + 1.5(2j) + j + j + 1.5j = 21 3 3 3 4
10.5j = 21 2j + πj = 4(4π + 6)
3
j = 2 cm 6j + 4πj = 12(4π + 6)
j(6 + 4π) = 12(4π + 6)
j = 12 cm

6. Tentukan perimeter bagi tembereng berlorek berdasarkan maklumat yang diberi.
Determine the perimeter of the shaded segment based on the given informations. TP 4

Contoh/Example (a) (b)
P K
A 11.2 cm
8.2 cm O j 8.5 cm

O 1.2 rad
2.3 rad
1.5 rad
B O
L
Q
2.3 rad = 2.3 × 180° j(1.5) = 8.5
π
1.2 rad = 1.2 × 180° j = 5.67 cm
π = 131.78° 1.5 rad = 1.5 × 180°
= 68.75° Panjang perentas PQ π
Panjang perentas AB = ! 11.2 + 11.2 – 2(11.2) kos 131.78° = 85.94°
2
2
2
Length of chord AB = ! 418.034 Panjang perentas KL
2
2
2
= ! 8.2 + 8.2 – 2(8.2) kos/cos 68.75° = 20.45 cm = ! 5.67 + 5.67 – 2(5.67) kos 85.94°
2
2
2
= ! 85.74 Panjang lengkok PQ = ! 59.745
= 9.26 cm = 11.2 × 2.3 = 7.73 cm
Panjang lengkok AB = 25.76 cm Perimeter
Length of arc AB Perimeter = 7.73 + 8.5
= 8.2 × 1.2 = 25.76 + 20.45 = 16.23 cm
= 9.84 cm = 46.21 cm
Perimeter
= 9.84 + 9.26
= 19.1 cm

Tip SPM

Gunakan petua kosinus.
Use the cosine rule.
a = b + c – 2bc kos q
2
2
2
a = b + c – 2bc cos q
2
2
2

6

01 Modul Series MateTam Tg5.indd 6 04/10/2021 2:15 PM