Modul Sukatan Membulat 1.2 Panjang Lengkok Suatu Bulatan v3

MATEMATIK TAMBAHAN
( ADDITIONAL MATHEMATICS)

SUKATAN MEMBULAT
( CIRCULAR MEASURE)

1.2 PANJANG LENGKUNG SUATU BULATAN

ARC LENGTH OF A CIRCLE

Menentukan perimeter tembereng suatu bulatan

Determining the perimeter of segment of a circle

DISEDIAKAN OLEH :

MOHD NOR FADHLI BIN AZIZ
JAMIL BIN TARMIZI
FAZIRA BINTI MOKHTAR
NURHIDAYAH BINTI ISMAIL

1.2 PANJANG LENGKOK SUATU BULATAN
ARC LENGTH OF A CIRCLE

(1.2.2-Menentukan perimeter tembereng suatu bulatan)
(1.2.2-Determining the perimeter of segment of a circle)

Nota

Untuk mencari panjang Perentas / To find the chord
θ

Formula 1: 2 j sin
2

Formula 2 : Petua Kosinus : j2  j2  2 j  jcosθ

Formula 3 : Petua Sinus AB  j B ; AB  j sin θ
sin θ sin sin B

1. Hitungkan perimeter tembereng berlorek bagi setiap rajah berikut : TP3
Calculate the perimeter of shaded segment in each of the folloing diagrams. TP3

(a-i)

Panjang perentas / length of chord

2   210sin 120 
j sin
22

Panjang lengok / arc length

s  10 1200  π  
1800 

Perimeter tembereng kawasan berlorek / the perimeter of shaded segment

[38.26 cm]

(a-ii)

Panjang perentas / length of chord

102 102  21010cos120 

Panjang lengok / arc length

s  10 1200 π  
 

1800

Perimeter tembereng kawasan berlorek / the perimeter of shaded segment

Modul Sukatan Membulat / Circular Measure_T5 [38.26 cm]
Page 1

(a-iii)

Panjang perentas / length of chord
10sin1200 
sin 300

Panjang lengok / arc length

s  10 1200 π  
 

1800

Perimeter tembereng kawasan berlorek / the perimeter of shaded segment

(b – i) [38.26 cm]

Panjang perentas / length of chord [9.909 cm]

2 j sin   2 sin 58  [9.909 cm]
[9.909 cm]
22
Page 2
Panjang lengok / arc length

s    π  
 1800 

Perimeter tembereng kawasan berlorek / the perimeter of shaded segment

(b – ii)

Panjang perentas / length of chord

 2   2  2  cos580 

Panjang lengok / arc length

s    π  
 1800 

Perimeter tembereng kawasan berlorek / the perimeter of shaded segment

(b – iii)

Panjang perentas / length of chord

 sin 580


sin 610

Panjang lengok / arc length

s    π  
 1800 

Perimeter tembereng kawasan berlorek / the perimeter of shaded segment

Modul Sukatan Membulat / Circular Measure_T5

(c – i)

Panjang perentas / length of chord
2 j sin  

2

Panjang lengok / arc length
s

Perimeter tembereng kawasan berlorek / the perimeter of shaded segment

(c – ii) [18.43 cm]
[18.43 cm]
Panjang perentas / length of chord

r2  r2  2rrcosθ 

Panjang lengok / arc length
s

Perimeter tembereng kawasan berlorek / the perimeter of shaded segment

(c – iii)

Panjang perentas / length of chord

 sin   
sin  

Panjang lengok / arc length
s

Perimeter tembereng kawasan berlorek / the perimeter of shaded segment

Modul Sukatan Membulat / Circular Measure_T5 [18.43 cm]
Page 3

(d – i)

Panjang perentas / length of chord
Panjang lengok / arc length

Perimeter tembereng kawasan berlorek / the perimeter of shaded segment

[17.08 cm]

(d – ii)

Panjang perentas / length of chord

Panjang lengok / arc length

Perimeter tembereng kawasan berlorek / the perimeter of shaded segment

(d – iii) [17.08 cm]
Panjang perentas / length of chord

Panjang lengok / arc length

Perimeter tembereng kawasan berlorek / the perimeter of shaded segment

Modul Sukatan Membulat / Circular Measure_T5 [17.08 cm]
Page 4

2. Sebuah bulatan berjejari 9 cm dan mempunyai satu perentas yang mencankum sudut
760 di pusat bulatan itu. Hitung perimeter tembereng minor itu. TP3
A circle of radius 9 cm has a chord which subtends an angle of 760 at the centre of
the circle. Calculate the perimeter of the minor segment. TP3

[23.02 cm]
3. Rajah menunjukkan sektor AOB berpusat di O. Panjang jejari ialah 2 kali ganda panjang

lengkok AB dan OB = 10 cm. TP4
The following diagram shows a sector AOB with centre O. The length of the radius is twice
the length of the arc AB and OB = 10 cm. TP4

Cari perimeter kawasan berlorek. / Find the perimeter shaded segment.

Modul Sukatan Membulat / Circular Measure_T5 [9.948 cm]
Page 5

4. Rajah menunjukkan sebuah sektor bulatan OPQ berpusat O. TP4
Diagram shows a sector of the circle OPQ centre O. TP4

Diberi OP = PQ, hitung perimeter kawasan berlorek.
Given that OP = PQ, calculate the perimeter shaded region.

Modul Sukatan Membulat / Circular Measure_T5 [18.43 cm]
Page 6