# Regular pentagonal pyramid

A regular pentagonal pyramid is a geometric solid that has a pentagonal base and five triangular faces that meet at a single point called the apex. All the faces of the pyramid are identical isosceles triangles. Here’s the information needed to calculate the surface area and volume of a regular pentagonal pyramid:

• Side length of the base (l)
• Apothem of the base (a), which is the distance from the center of the pentagon to the midpoint of any side of the pentagon
• Height of the pyramid (h), which is the distance from the apex to the base along a perpendicular line

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

A = (5/4) × l² × √(25 + 10 × √5) × h²

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

V = (5/12) × l² × h × √(5 – 2 × √5)

Steps to Calculate Surface Area and Volume:

1. Calculate the apothem of the pentagonal base using the formula: a = (l/2) × √(5 – 2 × √5)
2. Calculate the surface area of the pentagonal pyramid using the formula: A = (5/4) × l² × √(25 + 10 × √5) × h²
3. Calculate the volume of the pentagonal pyramid using the formula: V = (5/12) × l² × h × √(5 – 2 × √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.