rea, permetro y volumen de figuras del plano y del espacio www.vaxasoftware.com A = rea, P = Permetro, V = Volumen Figuras del plano

Cuadrado

2aA = = 90 interno ngulo

aP 4= = 90 externo ngulo 2 diagonales Nm. =ND

Rectngulo

hbA =

hbP 22 +=

Paralelogramo

hbA =

abP 22 +=

Rombo

2DdA =

aP 4=

2224 Dda +=

Trapecio

hBbA2+=

cBbaP +++=

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Trapecio recto

hBbA2+=

hBbaP +++=

222 )( hbBa +=

Tringulo equiltero

2

43

2 ahaA == = 60 interno ngulo

aP 3= =120 externo ngulo ah

23= 0 diagonales Nm. =ND

Tringulo issceles

2sen

2 AbahbA ==

baP += 2 , Aah sen =

222 44 bha +=

Tringulo escaleno

2hbA =

))()(( csbsassA = 2

cbas ++=

cbaP ++= CaAch sen sen ==

Tringulo rectngulo

2abA = BcAca cos sen ==

cbaP ++= AcBcb cos sen ==

222 bac +=

Pentgono regular

=+== 72sen 255210

85

25 22 rrbaA

bP 5= 222 44 bar += =108 interno ngulo == 36sen 25210

2rrb = 72 externo ngulo

=+= 36 cos5264

rra 5 diagonales Nm. =ND

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Hexgono regular

== 06sen 32

33 22 bbA =120 interno ngulo bP 6= = 60 externo ngulo

== 30cos23 bba 9 diagonales Nm. =ND

Octgono regular

( )12

25,22tan

2 8282,52 tan8422

22

=====bbaabaA

== 5,22tan168 abP =135 interno ngulo

= 5,22cosra = 45 externo ngulo = 2,52sen2rb 20 diagonales Nm. =ND

Polgono regular de n lados

nanbanA == 180 tan

2 2

nn = 180)2(

:interno ngulo

nanbnP == 180tan2 =180

:externo ngulo

nra = 180cos

nrb = 180sen2

2)3(

:diagonales Nm.= nnND

Crculo

2 rA =

rP 2=

Sector circular

= 360 2 rA

= 180 rL

LrP += 2 en grados sexagesimales

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Segmento circular

= 2sen

3602 rA

=2

cos1 rh 2

sen2 rc = = 180 rL

cLP += hchr82

2

+= en grados sexagesimales

Tringulo circular

2sen 2 rA =

2sen2 rc =

crP += 2 en grados sexagesimales

Trapecio circular

( ) = 360 22 rRA

)(2360

)( 2 rRrRP ++=

en grados sexagesimales

Corona circular

( )22 rRA =

)( 2 rRP +=

Elipse

baA =

)( baP +

+= 2/0 2222 cossen4 dttbtaP

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Figuras del espacio Cubo (hexaedro)

2 6 aA =

3aV =

Prisma recto

cbcabaA 222 ++=

cbaV =

Esfera

24 rA =

34 3rV =

Cilindro

)( 2 rhrATOTAL +=

2 2 rABASES = hrALATERAL 2=

hrV 2=

Cono

2 rgrATOTAL +=

2 rABASE = grALATERAL =

3 2 hrV = 222 rhg +=

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Pirmide

BASELATTOTAL AAA +=

2Permetro CBASE

LAThA =

3hAV BASE=

Segmento esfrico

BASECURVASUPTOTAL AAA += .

4 2cABASE = ( )22. 4 4 2 hchrA CURVASUP +==

=

+=

3

43

6 222 hrhhchV

hchr82

2

+=

Toro

)( 2222 rRdDA ==

22

22

))((4

4

rRrRdDV +==

rRD += , rRd =

Tetraedro

2 3 aA =

2 43 aACARA = ahC 2

3= ah36=

3 12

2 aV =

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Octaedro

2 32 aA =

2 43 aACARA =

3 32 aV =

Dodecaedro

2 510253 aA +=

2 4

51025 aACARA+=

3 4

5715 aV += Icosaedro

2 35 aA =

2 43 aACARA =

( ) 3 53 125 aV +=

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