a regular pentagonal prism has an apothem of 5. find the surface area and volume

Question

ddcamp · Answer

Here's one base:
|dw:1368832966562:dw|

Do you know how to find x°?

anonymous · Answer

Yes, I do. It's 54 degrees

ddcamp · Answer

With that, you know that tan(54°) = 5/(half the side length)

You can then find the area of the triangle, and then the area of the pentagon.

ddcamp · Answer

SA = 2(Area of Pentagon) + 5(side length)(height)
V = (Area of Pentagon)(height)

anonymous · Answer

Okay thanks. Do you know how to find the height of the prism because don't you need that to find both the surface area and the volume? That's like really the only part I'm confused about

ddcamp · Answer

Good question. I think you just need to solve in terms of h. The height could be anything and it would still be a regular pentagonal prism.

anonymous · Answer

Alright thank you. I will try that.