# Regular triangular pyramid

A regular triangular pyramid is a three-dimensional solid with a base that is an equilateral triangle and three congruent triangular faces that meet at a single point called the apex. Here’s the information needed to calculate the surface area and volume of a regular triangular pyramid:

• Length of a side of the base (l)
• Height of the pyramid (h)

Formula for Slant Height: The slant height (s) of a regular triangular pyramid can be calculated using the Pythagorean theorem:

s = √(l² – (h/2)²)

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

A = (l²√3)/4 + 3 × (l × s)/2

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

V = (l²h)/12√2

Steps to Calculate Surface Area and Volume:

1. Determine the length of a side of the base (l).
2. Determine the height of the pyramid (h).
3. Calculate the slant height of the pyramid using the formula: s = √(l² – (h/2)²)
4. Calculate the surface area of the regular triangular pyramid using the formula: A = (l²√3)/4 + 3 × (l × s)/2
5. Calculate the volume of the regular triangular pyramid using the formula: V = (l²h)/12√2

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.