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Strangerrr

Member

Registered: 2018-07-28

Posts: 23

Area and Volume of Prisms and Pyramids

The area and volume of the given shape, if the length of one side of the base is 6, the height of the pyramid/prism is 8, and the slant height is 10.

the base of the prism is an isosceles triangle with a base of 4 and sides of 6

A Lateral area: 128;  Volume: 64√(2)
B Lateral area: 120;  Volume: 240
C Lateral area: 240;  Volume: 144
DLateral area: 176;  Volume: 64√(2)
E Lateral area: 160;  Volume: 192
F Lateral area: 240;  Volume: 64

4(6) = 24
24*10 = 240

4(6) = 24
24(6) = 144

C Lateral area: 240;  Volume: 144

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,413

Re: Area and Volume of Prisms and Pyramids

Hi Strangerrr,

See Prisms and Pyramids.

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Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Area and Volume of Prisms and Pyramids

hi Strangerrr

I'm not getting that answer.  Imagine the prism made from card.  If you unfold the net you'd have two triangular ends and three rectangles.  The lateral area is the area of those three rectangles.  Their measurements are 4 by 8, 6 by 8 and 6 by 8.

To get the volume you need the area of the triangle and then times by the height (8).

The perpendicular height of the triangle requires Pythag: sq rt (6^2 - 2^2).    2 because you make a right angle by dividing the isosceles triangle in half.

The 'slant' height isn't needed for prisms … they don't have one.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Strangerrr

Member

Registered: 2018-07-28

Posts: 23

Re: Area and Volume of Prisms and Pyramids

L = Ph

= 16*8

= 128

H^2 + H^2 = 6^2

H^2 + 4 = 36

- 4 -4

H^2 = 32

H = √32

H = √16 * √2

= 4√ 2

Base = 4

Height = 4√2

Area = 1/2 * base * height

= 1/2*4^2* 4√ 2

= 8√ 2

V = Bh

= 8√ 2 * 8

64 √2

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Area and Volume of Prisms and Pyramids

That's exactly what I got!

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob