Question

The two triangular prisms shown are similar.

Answer 1

144m^3 im taking the test rn 

Answer 2

The answer is D.) $144 m^{3}$

The formula for a triangular prism is $V=\frac{1}{2}a*c*h$

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

$V= \frac{1}{2} 1.5*1.5*2$

This would equal to $2.25m^{3}$ 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

$V=\frac{1}{2}6*6*8$
$V=3*6*8$
$V=18*8$

and our answer:

$V=144 m^{3}$

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