figu2d3d
TRANSCRIPT
-
7/26/2019 figu2d3d
1/7
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 +++=
www.vaxasoftware.com
http://www.vaxasoftware.com/indexes.htmlhttp://www.vaxasoftware.com/indexes.htmlhttp://www.vaxasoftware.com/indexes.htmlhttp://www.vaxasoftware.com/indexes.html -
7/26/2019 figu2d3d
2/7
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
www.vaxasoftware.com
http://www.vaxasoftware.com/indexes.htmlhttp://www.vaxasoftware.com/indexes.html -
7/26/2019 figu2d3d
3/7
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
www.vaxasoftware.com
http://www.vaxasoftware.com/indexes.htmlhttp://www.vaxasoftware.com/indexes.html -
7/26/2019 figu2d3d
4/7
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
www.vaxasoftware.com
http://www.vaxasoftware.com/indexes.htmlhttp://www.vaxasoftware.com/indexes.html -
7/26/2019 figu2d3d
5/7
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 +=
www.vaxasoftware.com
http://www.vaxasoftware.com/indexes.htmlhttp://www.vaxasoftware.com/indexes.htmlhttp://www.vaxasoftware.com/indexes.htmlhttp://www.vaxasoftware.com/indexes.htmlhttp://www.vaxasoftware.com/indexes.html -
7/26/2019 figu2d3d
6/7
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=
www.vaxasoftware.com
http://www.vaxasoftware.com/indexes.htmlhttp://www.vaxasoftware.com/indexes.html -
7/26/2019 figu2d3d
7/7
Octaedro232 aA =
24
3aACARA =
3
3
2aV=
Dodecaedro2510253 aA +=
24
51025aACARA
+=
34
5715aV
+=
Icosaedro 235 aA =
24
3aACARA =
( ) 35312
5aV +=
www.vaxasoftware.com
http://www.vaxasoftware.com/indexes.htmlhttp://www.vaxasoftware.com/indexes.html