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rea, permetro y volumen de f iguras del plano y del espacio www.vaxasoftware.com

A = rea, P = Permetro, V = Volumen

Figuras del plano

Cuadrado 2aA= = 90internongulo

aP 4= = 90externongulo

2diagonalesNm. =ND

RectngulohbA =

hbP 22 +=

ParalelogramohbA =

abP 22 +=

Rombo2DdA =

aP 4=

2224 Dda +=

Trapecio

hBb

A2

+=

cBbaP +++=

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Trapecio recto

hBb

A2

+=

hBbaP +++= 222 )( hbBa +=

Tringulo equiltero2

4

3

2

a

haA == = 60internongulo

aP 3= =120externongulo

ah2

3= 0diagonalesNm. =ND

Tringulo issceles

2

sen

2

AbahbA ==

baP += 2 , Aah sen=

222 44 bha +=

Tringulo escaleno

2

hbA =

))()(( csbsassA = 2

cbas

++=

cbaP ++= CaAch sensen ==

Tringulo rectngulo

2

abA= BcAca cossen ==

cbaP ++= AcBcb cossen ==

222 bac +=

Pentgono regular

=+== 72sen2

55210

8

5

2

5 22 rrba

A

bP 5= 222 44 bar += =108internongulo

== 36sen252102

rr

b = 72externongulo

=+= 36cos5264

rr

a 5diagonalesNm. =ND

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Hexgono regular== 06sen3

2

33 22 bbA =120internongulo

bP 6= = 60externongulo

== 30cos2

3bba 9diagonalesNm. =ND

Octgono regular( )

12

2

5,22tan

28282,52tan84

2222

=

====

bbaabaA

== 5,22tan168 abP =135internongulo

= 5,22cosra = 45externongulo

= 2,52sen2rb 20diagonalesNm. =ND

Polgono regular de nlados

nan

banA

==

180tan

2

2

nn

= 180)2(

:internongulo

nanbnP

==

180tan2

=180

:externongulo

nra

=

180cos

nrb

=

180sen2

2

)3(

:diagonalesNm.

=

nnND

Crculo 2rA=

rP 2=

Sector circular

=

360

2 rA

=

180

rL

LrP += 2 en grados sexagesimales

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Segmento circular

=

2

sen

360

2 rA

=

2cos1

rh 2

sen2

rc=

=180

rL

cLP +=

h

chr

82

2

+= en grados sexagesimales

Tringulo circular

2

sen2 rA = 2

sen2

rc=

crP += 2 en grados sexagesimales

Trapecio circular ( )

=360

22 rRA

)(2360

)(2 rRrRP +

+=

en grados sexagesimales

Corona circular ( )22 rRA =

)(2 rRP +=

ElipsebaA =

)( baP +

+=2/

02222 cossen4 dttbtaP

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Figuras del espacio www.vaxasoftware.com

Cubo (hexaedro) 26 aA =

3aV=

Prisma rectocbcabaA 222 ++=

cbaV =

Esfera 24 rA =

3

4 3rV=

Cilindro )(2 rhrATOTAL +=

22 rABASES= hrALATERAL 2=

hrV 2=

Cono 2 rgrATOTAL +=

2 rABASE= grALATERAL =

3

2 hrV= 222 rhg +=

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PirmideBASELATTOTAL AAA +=

2

Permetro CBASELAT

hA =

3

hAV BASE=

Segmento esfricoBASECURVASUPTOTAL AAA += .

4

2cABASE= ( )22. 44

2 hchrA CURVASUP +==

=

+=

3

4

3

6

222

hrhh

chV

h

chr

82

2

+=

Toro)( 2222 rRdDA ==

22

22

))((4

4

rRrRdDV +==

rRD += , rRd =

Tetraedro 2

3aA=

24

3aACARA = ahC 2

3= ah

3

6=

312

2aV=

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Octaedro232 aA =

24

3aACARA =

3

3

2aV=

Dodecaedro2510253 aA +=

24

51025aACARA

+=

34

5715aV

+=

Icosaedro 235 aA =

24

3aACARA =

( ) 35312

5aV +=

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