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# ¿ejercicios de geometria?

calcular el area total y volumen de un prisma de base cuadrangular cuyas medidas son:
13 cm de largo, 6 cm de ancho, 9 cm de alto.

calcular area total y volumen de un poliedro de base cuadrada cuyo apotema basal mide 6 cm y apotema lateral 10 cm.

10 puntos a quien me ayude por fas!!!!!
Member since:
May 15, 2009
Total points:
806 (Level 2)

## Best Answer - Chosen by Voters

A(Base) = 6 x 13 = 78 cm^2

A(lateral) = 2 rectangulos(6x9) + 2rectangulos(13x9)
A(lateral) = 2(6 x 9) + 2( 13 x 9) = 108 + 234 = 342 cm^2

A(total) = 2A(base) + A(lateral) =156 + 342 = 498

At = 498 cm ^2

V = A(base) x H (altura)

V = 78 x 9

V = 702 cm^3

Ej.2 PIRAMIDA

apotema basal --->a = 6cm
apotema lateral --->a'=10cm

Si a = 6 cm resulta L = 2 x a =12cm .... L->lado cuadrdo

resulta A(base) = L^2 = 12 x12 =144 cm^2

A(lateral) = 4 x A(triangulo isoscel)

Atriangulo = base x h /2

h = apotema lateral =a' =10

resulta A(tringulo) = L x a' /2=12 x 10/2 =60

resulta A(lateral) = 4 x 60 = 240

resulta At = 240 + 144 = 384

V = A(base) x H(altura piramida)/3
_____________________
Pitgora : H^2 + a^2 = a' ^2 |

H^2 = 100 - 36 = 64

H = raiz(64) = 8
_____________________|

resulta V = 144 x 8/3

V = 1152/3 cm^3

V = 384 cm^3

A ver !!! ¿donde estan MIS PUNTOS ?????
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• Member since:
February 20, 2007
Total points:
62,724 (Level 7)
Estimado amigo, en el siguiente link se ilustran ambas figuras (por favor aumenta el zoom):

http://img44.imageshack.us/img44/9673/ej…

Area total del prisma = Atp = 2(13)(6)+2(6)(9)+2(13)(9) = 498 cm²

Volumen del prisma = Vp = (13)(6)(9) = 702 cm³

Area total de la pirámide = Atpi = [(Apb)(2)]² + 4[2(Apb)(Apl)/2] =>
Atpi = (12)² + 4(6)(10) =>
Atpi = 144 + 240 =>
Atpi = 384 cm²

Volumen de la pirámide = Vpi = {[Apb(2)]²(h)} / 3

debemos calcular h, para lo cual utilizamos el Teorema de Pitágoras:

(Apl)² = (Apb)² + h² =>
h² = (Apl)² - (Apb)² =>
h = √[(Apl)² - (Apb)²] =>
h = √[(10)² - (6)²] =>
h = √(100 - 36) =>
h = √(64) =>
h = 8 cm

ahora continuamos con el cálculo del volumen de la pirámide:

Vpi = {[6(2)]²(8)} / 3 =>
Vpi = 1152 / 3 =>
Vpi = 384 cm³

Espero haber podido ayudarte. Saludos!

### Source(s):

33% 1 Vote
• Member since:
April 27, 2009
Total points:
314 (Level 2)
Problema nº 1

a) Calculo de area total.

Areas laterales = (largo * alto) * 4

Areas laterales = (13 cm * 9 cm) * 4 = 468 cm^2

Areas de plantas = (largo * ancho) * 2

Areas de plantas = (13 cm * 6 cm) *2 = 156 cm^2

Area TOTAL = 468 cm^2 + 156 cm^2 = 624 cm^2

AREA TOTAL = 624 cm^2

b) Calculo de volumen

Vol = (Largo * Ancho * Alto) = (13 cm * 6 cm * 9 cm) = 702 cm^3

VOL.= 702 cm^3
• by Marisol
Member since:
June 29, 2009
Total points:
247 (Level 1)
kee wevaa
jojo