Mensuration by singaraj

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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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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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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