Frmulas de rea, permetro y volumen de figuras del plano y del espacio

A = rea, P = Permetro, V = Volumen

Figuras del planoCuadrado A = a 2 ngulo interno = 90P = 4a ngulo externo = 90Nm. diagonales ND = 2

Rectngulo A = bh P = 2b + 2h

Paralelogramo A = bh P = 2b + 2a

Rombo d D A =2P = 4a4a 2 = d 2 + D 2

TrapecioA = b + B h2P = a + b + B + c

www.vaxasoftware.comTrapecio rectoA = b + B h2P = a + b + B + ha2 = (B b)2 + h2

Tringulo equilteroA = ah = 3 a 2 ngulo interno = 602 4P = 3a ngulo externo = 120h = 3 a Nm. diagonales ND = 02

Tringulo issceles bh absen A A = =2 2P = 2a + b , h = a sen A4a 2 = 4h2 + b2

Tringulo escaleno bhA =2A = s(s a)(s b)(s c) s = a + b + c2P = a + b + c h = c sen A = a sen C

Tringulo rectngulo baA = a = c sen A = c cos B2P = a + b + c b = c sen B = c cos Ac 2 = a 2 + b2

Pentgono regularA = 5ab = 5 r 2 10 + 2 5 = 5 r 2 sen 722 8 2P = 5b 4r 2 = 4a 2 + b2 ngulo interno = 108b = r 10 2 5 = 2rsen 36 ngulo externo = 722a = r 6 + 2 5 = rcos 36 Nm. diagonales ND = 54

www.vaxasoftware.comHexgono regular 3 3 2 2A = b = 3b sen 60 ngulo interno = 1202P = 6b ngulo externo = 60a = 3 b = bcos 30 Nm. diagonales ND = 92

Octgono regular ( ) 2b 2 2b 2

A = 4ab = 8a2 tan 22,5 = 8 2 8 a2 = =tan 22,5 2 1P = 8b = 16atan 22,5 ngulo interno = 135a = rcos 22,5 ngulo externo = 45b = 2rsen 22,5 Nm. diagonales ND = 20

Polgono regular de n lados ngulo interno :A = nab = na 2 tan 180 (n 2)1802 n =nP = nb = 2natan 180 ngulo externo :n = 180 Nm. diagonales :a = rcos 180 b = 2rsen 180 n(n 3)n n ND =2

Crculo A = r 2 P = 2 r

Sector circularA = r 2 360L = r 180P = 2r + L en grados sexagesimales

www.vaxasoftware.comSegmento circularA = r 2 sen 360 2 h = r1 cos c = 2rsen L = r 2 2 180h c 2P = L + c r = + en grados sexagesimales2 8h

Tringulo circular sen A = r 2 c = 2rsen2 2P = 2r + c en grados sexagesimales

Trapecio circularA = (R 2 r 2 ) 360P = 2 (R + r ) + 2(R r )360 en grados sexagesimales

Corona circular A = (R2 r 2 ) P = 2 ( R + r )

Elipse A = abP (a + b)P = 4 / 2 a2sen2t + b2 cos2 t dt0

www.vaxasoftware.comCubo (hexaedro) A = 6 a 2 V = a3

Prisma recto A = 2ab + 2ac + 2bc V = abc

Esfera A = 4r 24r 3V =3

Cilindro A = 2 r (h + r)TOTALA = 2 r 2 A = 2 rhBASES LATERALV = r 2 h

Cono A = rg + r 2TOTALA = r 2 A = rgBASE LATERAL r 2 hV = g 2 = h2 + r 23

www.vaxasoftware.comPirmide

ATOTAL = ALAT + ABASEA = Permetro BASE hC LAT 2V = ABASE h3Segmento esfrico

ATOTAL = ASUP.CURVA + ABASEABASE =

c2

A . = 2 rh =

(c2

+ 4h2 )4 SUP CURVA 4 3c 2

2 h

h c 2V = h 6 4

+ h = h

r 3

r = +2 8h Toro

A = 2 Dd = 2 (R2 r 2 )V =

Dd 2 =

(R + r )(R r)24 4

D = R + r ,

d = R rTetraedro

A = 3 a2A = 3 a 2

h = 3 a

h = 6 aCARA 4 C 2 3

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V = 2 a312Octaedro

A = 2

ACARA

3 a2= 3 a 24V = 2 a33Dodecaedro

A = 3

25 + 10

5 a 2ACARA

= 25 + 10 5 a24V = 15 + 7 5 a34Icosaedro

A = 5

ACARA

3 a2= 3 a 24

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V = 5 (3 +12

5 )a3

2

2

2