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7/18/2019 Perimeter and Area Cem
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O
θ
B
A
r
TOPIC : AREA AND PERIMETER
NOTES :
1. Perimeter of a circle =r π 2
2. Area of a circle =
2r π
3. Arc length AB =
r x π θ
2360
4. Area of sector =
2
360r x π
θ
5. The perimeter of a closed shape is the total length of the outer boundary that encloses
the shape.
7/18/2019 Perimeter and Area Cem
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EXAMPLE 1
In diagram 1, OABC is a sector of a circle ith centre O and radi!s 1" cm. #i$en that
∠
B%&=
ο 60
'IA#(A) 1
B* !sing+
22=π
, calc!late
a- perimeter, in cm, the shaded area.- area, in cm2, the shaded area.
/+markah
Answer :
a - AB =
22 1"1" +
=
32
= 1.0 / 1 mar
Perimeter = Arc 4ength AC 1" 1" 1.0
=
1"
+
222
360
150×××
1" 1" 1.0 /1 mar
="."+or
Arc 4ength AB Arc 4ength B& 1" 1" 1.0 /1 mar
1"+
222
360
0×××
1"+
222
360
60×××
1" 1" 1.0
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O
AB
CD
DIAGRAM 1
="."+ cm /1 mar
-
21"+
22
360
150××
1"1"2
1××
ata! /2mar
=3
++0
7
=3
215
ata!3
"+6
ata! 15.6+ /1 mar
EXERCISE
. In 'iagram 1, ABD is an arc of a sector ith the centre O and BCD is a 8!adrant.
OD = OB = 1" cm and
"5 AOB∠ = o
.
9sing+
22=π
, calc!late
a- the perimeter, in cm, of the hole diagram,
- the area, in cm2, of the shaded region.
/6 marks
Answer :
7/18/2019 Perimeter and Area Cem
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T
Q 14 cm
7 cm
R
S
a-
-
2. 'iagram 2 shos to sectors OPQ and ORS , oth ith centre O.
It is gi$en that∠
POQ = 60°.
B* !sing π =+
22
, calc!late
a- the perimeter, in cm, of the hole diagram,
- the area, in cm2, of the shaded region.
/ 6 mars
Answer :
a-
'IA#(A) 2
O
P
7/18/2019 Perimeter and Area Cem
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A O B
F
C
D
E
DIAGRAM 3
-
3. 'iagram 3 shos to semicirles AOBCE and OBCD, ith the centre O and B respecti$el*.
BFC is a sector ith the centre B. AOBC is a straight line and AO = 2OB.
BC = 3.5 cm and∠
FBC =∠
AOE = 60;. 9singπ
=+
22
, calc!late
(a) the perimeter, in cm, of the hole diagram,
(b) the area, in cm
2
, of the shaded region. /6 marks
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Answer:
(a)
(b)
4. In 'iagram ", ABCD is a rectangle. #i$en that AC is the diameter of a semicircle AFBGC .
CDHE is a 8!adrant ith centre C .
A
B
C
D
E
F
G
H
'iagram "
7/18/2019 Perimeter and Area Cem
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A BO
210o
B
9singπ
=+
22
, calc!late
a- the perimeter, in cm, of the hole diagram. /3 marks
- the area, in cm
2
, of the shaded region. /3 marks
Answer :
(a)
(b)
5. In 'iagram 5, the shaded region represents the part of the flat indscreen of a $anhich is eing iped * the indscreen iper AB. The iper rotates thro!gh an
angle of 210o ao!t the centre O. #i$en that OA = + cm and AB = 2 cm.
7/18/2019 Perimeter and Area Cem
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Diagram 6
Rajah 6
30
M !
"
#
4 cm
3 cm
30$
'IA#(A) 5
9sing π =+
22
, calc!late
i- the length of arc BB′ ,
() the ratio of arc lengths , AA′ : BB′
iii- the area of the shaded region. /+ marks
Answer :
i-
ii-
iii-
!. In 'iagram 6 , !" and #$ are arcs of centre % and ! respecti$el*. Da&am Ra'ah !" *an #$ a&ah &en+k,k b-&aan ber/-sa * % *an ! masn+0masn+.
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O%
Q
R
S
1&0'7 cm
12 cm
DIAGRAM 7
7 cm
9sing
22+
π =
, calc!late
Den+an men++-nakan
22
+π =
h-n+
(a) the perimeter, in cm, of the hole diagram , /ermeer *a&am 1m se&-r-h ra'ah
(b) the area, in cm2, of the shaded region . &-as *a&am 1m2 kawasan ber&,rek .
/6 marks/6 markah
Anser< %awa/an:
(a)
(b)
". 'iagram + shos to sectors of circle ORQ and OPS ith centre O.
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O
R
S
T
(
)
Q
1200
B* !sing π =+
22
, calc!late
a- the perimeter, in cm, of the hole diagram.
- the area, in cm2, of the shaded region.
/ 6 marks
Answer :
a-
-
. 'iagram shos to sectors ORS3 and O45" ith the same centre O. OQ3 is a
semicircle ith centre 4 . #i$en O3 = 1" cm.
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A
B
O
D
C
E
4&0
'IA#(A)
9sing π = +
22
, calc!late
a- the perimeter, in cm, of the
hole diagram,
b- the area, in cm3, of the
shaded region..
/+ marks
Answer :
a-
b-
. In 'iagram , OAB is a sector of a circle ith centre O and CDE isanother circle ith centre %. #i$en that OD = AD = + cm
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Q
%
R
O
'IA#(A)
Ass!ming that π =+
22
, calc!late
i- the perimeter of the hole diagram.
ii- the area of the shaded region
/6 marks
Answer :
a- i-
ii-
#. 'iagram 10 shos a circle PQR ith center O and three semicircles .
#i$en that POQ = QOR = ROP and OP = OQ = OR = 2 cm .
Ra'ah 6 men-n'-kkan seb-ah b-&aan ber/-sa * O *an +a b-ah se/ar-h b-&aan. Dber bahawa POQ = QOR = ROP an* OP = OQ = OR = 27 1m .
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'iagram 10
9sing π =
+
22
, calc!late
Den+an men++-nakan π =+
22
, h-n+
a - the length of arc PQR
/an'an+ &en+k,k PQR
- the area of the shaded regions
&-as kawasan ber&,rek
/ 5 marks
Answer :
a-
-
ANS$ER :
TOPIC : AREA AND PERIMETER
1. a-
3
2+0
-
161
2. (a)
3.65<6
55
(b)
"2.1+"=12
51+"
3. (a)
231
3 ,r 68.9 (b) 67
2
1
1m2 ,r 67.; 1m2
7/18/2019 Perimeter and Area Cem
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" %a&
25.5-,+
33+ b
5 a- i-
33.12=3
112
- 1:5 c- 2156
6. a-
5.21=21
2021
-
3.23=6
523
+. a-
52.5+=21
115+
-
".122=21
10122
. a-
66+.+2=+
5+2
-
66+.1+=3
21+
. a- 63.5 - 12.5
10. (a)3
111+
,r <<.66 (b)3
2133"
,r <66.9
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