mensuration by singaraj
TRANSCRIPT
exit
Cuh£Á x‹¿a¤ bjhl¡f¥gŸë, br«gu«gh¡f«, óéUªjtšè x‹¿a«. n#. Á§fuh{, Ï.ã. MÁça®,
ÂUtŸS® kht£l«
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0
1
2
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l EIGHT UNITS
b FOUR UNITS
THE AREA OF RECTANGLE ABCD IS l b l b SQUARE UNITS
8 4 32THE AREA OF RECTANGLE ABCD IS SQUARE UNITS
RECTANGLE
bb
l
ll EIGHT UNITS
b FOUR UNITS
THE AREA OF RECTANGLE
ABCD IS l b lb SQUARE UNITS
8 4 32
RECTANGLE
THE AREA OF RECTANGLE
ABCD IS SQUARE UNITS
exit
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0
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0
1
2
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SQUARE
a
a
a a
SQUARE
aa a a2
4 4 16
SIDE OF SQUARE UNITS
AREA OF SQUARE SQUARE UNITS
SQUARE UNITSAREA OF SQUAREexit
b
PARALLELOGRAM
AREA OF PARALLELOGRAM IS AREA OF RECTANGLE
AREA OF PARALLELOGRAM IS
b b SQUARE UNITS
b UNITS
UNITS
BASE OF PARALLELOGRAM IS
HEIGHT OF PARALLELOGRAM IS THE PARALLELOGRAM CHANGE INTO RECTANGLE
THE BASE CHANGE INTO LENGTH OF THE RECTANGLE SO
exit
RHOMBUS
DIAGONALd1
DIAGONALd2
AREA OF RHOMBUS IS AREA OF THE RECTANGLE12_
12_ d1 d2 SQUARE UNITSAREA OF RHOMBUS IS
exit
b - BASE
AREA OF TRIANGLE AREA OF RECTANGLE
BASE ( b )
12_ h
12_ b h 12_ b h AREA OF TRIANGLE IS
SQUARE UNITS
THE TRIANGLE CHANGE INTO RECTANGLE
exit
b
a
TRAPEZIUM
AREA OF TRAPEZIUM ABCD IS
(AREA OF ABD ) (AREA OF BCD)
( AB ED) ( DC BF)12_ 1
2__
( a h)12_ 1
2__ ( b h)
( ah)12_ 1
2__ ( bh)
( a b) h12_AREA OF TRAPEZIUM
ABCD IS SQUARE UNITS
exit
hM1 M2
a
b
E
b
b
bb
bb
AREA OF TRAPEZIUM
AREA OF RECTANGLE
AREA OF TRAPEZIUM LENGTH BREADTH (a b) h 1
2_
12_ (a b) h SQUARE UNITS
AREA OF TRAPEZIUM
12_ h
rçtf«
exit
rçtf«
rçtf¤Â‹gu¥gsÎ
rçtf¤Â‹g©òfŸ
K¡nfhz§fshf m¿jš
br›tfkhfm¿jš
12_(a b) h rJu myFfŸ
xU nrho g¡f§fŸ k£L« Ïizahf
cŸs eh‰fu«
exit
exit
Cuh£Á x‹¿a¤ bjhl¡f¥gŸë, br«gu«gh¡f«, óéUªjtšè x‹¿a«. n#. Á§fuh{, Ï.ã. MÁça®,
ÂUtŸS® kht£l«
P = R‰wsÎ (PERIMETER) D = é£l« ( DIAMETER)
R‰wsÎ
t£lika«
é£l«
Mu«
Á¿a t£l
nfhz¥gFÂ
bgça t£lnfhz¥gFÂ
t£l«
t£l eh©
t£l eh©
t£l eh©
t£l eh©
t£l ¤Â‹ äf¥bgça eh© ( é£l«)
t£l eh©t£l eh©
t£l¤Â‹ ika¡nfhz« = 360 °.
t£l«
P
P = PERIMETER
D = DIAMETER
22 ▬ 7
3.14~▬ ~▬
2r = d
P▬ = πd
t£l¤Â‹ gç¡F« é£l¤Â‰F« ÏilnaÍŸs bjhl®ò
~▬ π
P = R‰wsÎ ( PERIMETER)
D =é£l« (DIAMETER)r =Mu« ( radius)
P = R‰wsÎ P = R‰wsÎ ( PERIMETER)
D =é£l« (DIAMETER)
2r = d
P▬ = πd
t£l¤Â‹ R‰wsÎ
t£l¤Â‹ R‰wsÎ
r =Mu« ( radius)
= πt£l¤Â‹ é£l«
t£l¤Â‹ R‰wsÎ
= π × t£l¤Â‹ é£l«
t£l¤Â‹ R‰wsÎ
= π × d
t£l¤Â‹ R‰wsÎ
= π ×
2r
t£l¤Â‹ R‰wsÎ
= 2πr rJu myFfŸ
P▬2
P▬2
rrA B
CD
AREA OF ABC
D= AREA OF
P▬2
r
=P▬2
× r
Multiply by ‘r’ on both side of numerator and denominator
=P▬2r
× r × r
2r = d
=P▬d
× r2
P▬ = πd
AREA OF = πr² s q units
miu t£l¤Â‹ R‰wsÎ
miu t£l¤Â‹ ika¡nfhz« 180 °
A Bomiut£l¤Â‹ R‰wsÎ
R‰wsÎ (P) = (½ × t£l¤Â‹ gç ) + (2 × Mu«)
P = (½ × 2πr ) + 2r
P = (πr +2r ) = ( π + 2) r r myFfŸ.
miut£l¤Â‹
R‰wsÎ = ( π + 2) r r myFfŸ.
180 °
P▬2
r r
miu t£l¤Â‹ gu¥gsÎ
A B
P▬2
r rmiut£l¤Â‹ gu¥gsÎ
miut£l¤Â‹ gu¥gsÎ (A) = ½ × t£l¤Â‹ gu¥gsÎ
= ½ × πr²
πr²
miut£l¤Â‹ gu¥gsÎ (A) = ▬ rJu myFfŸ. 2
fhš t£l¤Â‹ R‰wsÎ
fhš t£l¤Â‹ ika¡nfhz« 90 °A
B
ofhš t£l¤Â‹ R‰wsÎ
R‰wsÎ (P) = (¼ × t£l¤Â‹ gç ) + (2 × Mu«)
P = (¼ × 2πr ) + 2r
P = (πr +2r ) = ( π + 2) r r myFfŸ.
miut£l¤Â‹
R‰wsÎ = ( π + 2) r r myFfŸ.
90 °
P▬4
r
r
▬ 2
▬ 2
▬ 2
fhš t£l¤Â‹ gu¥gsÎ
fhš t£l¤Â‹ gu¥gsÎ
fhš t£l¤Â‹ gu¥gsÎ (A) = ¼ × t£l¤Â‹ gu¥gsÎ
= ¼ × πr²
πr²
fhš t£l¤Â‹ gu¥gsÎ (A) = ▬ rJu myFfŸ. 4
A
B
o
90 °
P▬4
r
r
r®trk K¡nfhz§fŸ
A
B C
P
Q RPQ
R
P
Q
RP
Q
R
A P
B Q
C R
gf;fk; AB = gf;fk; PQ;gf;fk; BC = gf;fk; QRgf;fk; CA = gf;fk; RP
Nfhzk; A = Nfhzk; PNfhzk; B = Nfhzk; QNfhzk; C = Nfhzk; R
SSS – mo¥gil¡ bfhŸif
A
B C
S – g¡f«
A – nfhz«
E F
D
P
S
R
Q
SAS – mo¥gil¡ bfhŸif S – g¡f«
A – nfhz«
A
B C
A
B C
D
E F
A
B
C
3 – brÛ
7– b
rÛ300
A
B
C
3 – brÛ
7– brÛ300
A
B
C
3 – brÛ7– b
rÛ30
0
A
B
C3 – b
rÛ
7– b
rÛ
30
0
A
B
C
3 – brÛ
7– brÛ
300
A
B
C
3 –
brÛ 7–
brÛ
300
A
B
C
3 – brÛ
7– b
rÛ30
0
A
B
6–brÛ
3–brÛ
o
C
D
6–brÛ
3–brÛ
o
C
D
6–brÛ
3–brÛ
o
C
D
6–brÛ
3–brÛ
o
ASA – mo¥gil¡ bfhŸif S – g¡f«
A – nfhz«
A
B C
A
B C
A
B C
RHS – mo¥gil¡ bfhŸif
D
E F
A
B C
D
E F
D
E F
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