Can you help me out please??

Question

so...i have a question on my math, and i can't figure it out and i think it's cause i don't have a diagram but here it is....

a right prism has a height of 34 cm. Its base is a regular decagon with a side length of 16.8. Find the surface area and volume of the prism.

if you could pleaz help me that'd be amazing!!!

thank you :D

Answer 1

The volume of a right prism of any constant cross-section equals the area of that cross-section times the height of the prism.

According to http://en.wikipedia.org/wiki/Decagon , the area A of a decagon of side "a" is given by

A = a² × 5√(5 + 2√5)/2 ≈ 7.6942a²

The lateral area of the prism consists of 10 rectangles whose width equals the side of the decagon and whose length equals the height of the prism. I suppose the area of the ends should be included as well, so to the total rectangular area add twice the area of the decagon, as given above, to find the total surface area.