# Regular pentagonal prism

A regular pentagonal prism is a three-dimensional geometric shape that has two identical pentagonal bases and five rectangular faces. The following information can be used to calculate the surface area and volume of a regular pentagonal prism:

• Side length of the pentagon base (l)
• Height of the pentagonal prism (h)

Formula for Surface Area: The surface area of a regular pentagonal prism can be calculated using the following formula:

A = 5 × l × h + 2 × (5/2 × l × s)

Where: A = Surface area of the pentagonal prism l = Length of one side of the pentagon base h = Height of the pentagonal prism s = Slant height of the pentagonal base, which can be calculated using the formula: s = l / (2 × sin(π/5))

Formula for Volume: The volume of a regular pentagonal prism can be calculated using the following formula:

V = (5/4) × l² × h × tan(π/5)

Where: V = Volume of the pentagonal prism l = Length of one side of the pentagon base h = Height of the pentagonal prism

Steps to Calculate Surface Area and Volume:

1. Calculate the slant height of the pentagonal base using the formula: s = l / (2 × sin(π/5))
2. Calculate the surface area of the pentagonal prism using the formula: A = 5 × l × h + 2 × (5/2 × l × s)
3. Calculate the volume of the pentagonal prism using the formula: V = (5/4) × l² × h × tan(π/5)

Note: π represents the mathematical constant pi, which is approximately equal to 3.14159.

I hope that helps you! Let me know if you have any further questions.