Área, perímetro y volumen de figuras
TRANSCRIPT
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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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