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isaacholton7
The answer is D.) [tex]144 m^{3} [/tex]

The formula for a triangular prism is [tex] V=\frac{1}{2}a*c*h [/tex]

a = the height of the base
c = the width of the base
h = the height of the actual prism

Let's match our values with the smaller prism to get an idea of what our formula will look like:

a = 1.5
c = 1.5
h = 2

[tex]V= \frac{1}{2} 1.5*1.5*2[/tex]

This would equal to [tex] 2.25m^{3} [/tex] when multiplied together

The question says that these prisms are similar, which means that the ratios between the sides of both of the prisms are the same.

So, the height and base width on the smaller one are the same, so for the bigger one they will be the same, 6. Now for the height. Let's first find our ratio between the lengths. to get from 1.5 to 6 we multiply by 4. Since all the ratios are the same, we can multiply 2 by 4 to find our height for our bigger prism which will be 8. Let's go ahead and get our variables for our bigger prism since we have all of our needed information:

a = 6
c = 6
h = 8

[tex] V=\frac{1}{2}6*6*8 [/tex]
[tex]V=3*6*8[/tex]
[tex]V=18*8[/tex]

and our answer:

[tex]V=144 m^{3} [/tex]

Thank you for the question!! I hope this helped! :) Have an amazing day :D

The Volume of the larger prism of the length of 6m, a width of 6m, and a height of 8m are 144 cubic meters.

What is the volume of the triangular prism?

The volume of the triangular prism is the product of half of the length, breadth, and height of the given prism.

Volume of triangular prism = 1/2 (length x width x height)

Volume of triangular prism = 1/2 (length x width x height)

= 1/2 ( a x c x h)

a = the height of the base

c = the width of the base

h = the height of the actual prism

For the smaller prism

a = 1.5

c = 1.5

h = 2

Volume of smaller prism = 1/2 ( a x c x h)

= 1/2 ( 1.5 x 1.5 x 2)

= 2.25 cubic meter

Now, we can see that the width of the smaller side is 1.5 cm and the width of the larger prism is 6 cm which is exactly equal to the 4 times the width of the smaller prism.

So, we can assume that all the side of the larger prism is equal to the 4 times sides of the smaller prism.

Therefore,

a = 6

c = 6

h = 8

Volume of larger prism = 1/2 ( a x c x h)

= 1/2(6 x 6 x 8)

= 144

Thus, the Volume of the larger prism is 144 cubic meters.

Learn more about triangular prism;

https://brainly.com/question/15843335

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