# Regular triangular pyramid calculator

# 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:**

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