If the dimensions of a pentagonal prism are quadrupled, then the surface area of the prism is multiplied by eight. true or false

Let's test it out.

Our first pentagonal prism will have a base edge length of 3 in and a height of 3 in.  One formula I found for the surface area of a pentagonal prism is , where a is the base edge length and h is the height.  I was able to simplify the term being multiplied to a²  like this:



The formula looks like this now:  .  We can plug in our values for a and h to find the surface area of the prism:



The surface area of our initial prism is approximately 76 in².  Let's quadruple the dimensions (a is 12 and h is 12) and plug them into the formula:



The surface area of the new prism is approximately 1215 in².  To finally answer this question, let's divide the second prism's surface area by the first's to see if we get 8.  The first prism's surface area should fit into the second's about 8 times if the statement is true:

1215 ÷ 76 ≈ 16

The statement is incorrect.  If the dimensions of a pentagonal prism are quadrupled, then the surface area of the prism is multiplied by ~16, not 8.

Agc and bgd are vertical angles