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(b) S (c)
P OR = 2OP Q
Perimeter rantau
berlorek
O
1.5 rad Perimeter of the shaded
region θ
j
= 21 cm R O j P
Q
Perimeter rantau berlorek
R
Perimeter of the shaded region
SP 1.2.2 2j + 2j + 1.5(2j) + j + j + 1.5j = 21 = 16π + 24
OP = OQ = QP
10.5j = 21 º q = 60° = π
j = 2 cm 3
π
π
2
j + πj + j + j + j = 16π + 24
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3 3 3
4
2j + πj = 4(4π + 6)
3
6j + 4πj = 12(4π + 6)
j(6 + 4π) = 12(4π + 6)
j = 12 cm

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

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

1.2 rad 2.3 rad
O
1.5 rad
O
B
L
Q 2.3 r(1.5) = 8.5
1.2 rad = 1.2 × 360° 2.3 rad = 2π × 360° r = 5.67 cm
2π = 131.78° 1.5 rad = 1.5 × 360°
= 68.75° Panjang perentas PQ 2π
Panjang perentas AB 2 2 2 = 85.94°
Length of chord AB = ! 11.2 + 11.2 – 2(11.2) kos 131.78° Panjang perentas KL
2
2
2
2
2
2
= ! 8.2 + 8.2 – 2(8.2) kos / cos 68.75° = ! 418.034 = ! 5.67 + 5.67 – 2(5.67) kos 85.94°
= ! 85.74 = 20.45 cm = ! 59.745
Panjang lengkok PQ
= 9.26 cm = 11.2 × 2.3 = 7.73 cm
Panjang lengkok AB / Length of arc AB = 25.76 cm Perimeter
= 8.2 × 1.2 Perimeter = 7.73 + 8.5
= 9.84 cm = 25.76 + 20.45 = 16.23 cm
Perimeter = 46.21 cm
= 9.84 + 9.26
= 19.1 cm

Tip SPM

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

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