Question

A right regular pentagonal prism has a base edge length 14 cm, and height 12 cm. Identify the volume of the prism to the nearest tenth. HELP PLEASE!!

Answer 1

4046.56 cm3

Explanation:

The base is made by 5 isosceles triangles, with one side of 14 cm, and the opposite angle of
`\frac{360} 5 = 72°`. Each of the other angle is
`\frac{180-72} {2} =54°`. From there, you can calculate the height of each base triangle as in
`\frac {h} 7 = tan54` or 9.634...cm.

Your volume will be
`5 * \frac  {(14 * 9.634)} 2 * 12 = 4046.56 cm^3`