Question

What is the volume of this triangular prism?

Answer 1

`V=5,676.16\ cm^(3)`

Explanation:

we know that

The volume of the triangular prism is equal to

`V=BL`

where

B is the area of the triangular face

L is the length of the triangular prism

Find the area of the triangular face B

`B=(1)/(2)(28*22.4)= 313.6\ cm^(2)`

we have

`L=18.1\ cm`

substitute the values

`V=313.6*18.1=5,676.16\ cm^(3)`

Answer 2

5676.16 cm^3

Explanation:

The volume of any prism is given by the formula ...

V = Bh

where B is the area of one of the parallel bases and h is the perpendicular distance between them. Here, the base is a triangle, so its area will be ...

B = 1/2·bh

where the b and h in this formula are the base and height of the triangle, 28 cm and 22.4 cm.

Then the volume is ...

V = (1/2·(28 cm)(22.4 cm))·(18.1 cm) = 5676.16 cm^3

_____

You will note that this is half the product of the three dimensions, so is half the volume of a cuboid with those dimensions. Perhaps you can see that if you took another such prism and placed the faces having the largest area against each other, you would have a cuboid of the dimensions shown.