The formula and steps for calculating the surface area and volume of a regular hexagonal pyramid.

A regular hexagonal pyramid is a pyramid with a hexagonal base and six congruent triangular faces that meet at a point at the top of the pyramid. Let’s assume that the pyramid is regular, which means that all sides of the hexagonal base are equal in length and all six triangular faces are congruent.

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

A = 3√3 × l² + 6 × l × h

Where: A = Surface area of the pyramid l = Length of one side of the hexagonal base h = Height of the pyramid

Steps to Calculate Surface Area:

1. Square the length of one side of the hexagonal base (l) to get l².
2. Multiply 3√3 by l² to get 3√3 × l².
3. Multiply 6 by l and h to get 6 × l × h.
4. Add 3√3 × l² and 6 × l × h to get the surface area of the regular hexagonal pyramid.

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

V = 1/3 × √3 × l² × h

Where: V = Volume of the pyramid l = Length of one side of the hexagonal base h = Height of the pyramid

Steps to Calculate Volume:

1. Square the length of one side of the hexagonal base (l) to get l².
2. Multiply l² and h to get l² × h.
3. Multiply √3 by l² × h to get √3 × l² × h.
4. Divide √3 × l² × h by 3 to get the volume of the regular hexagonal pyramid.

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