Triangular Pyramid Formula
A pyramid having a triangular base is called a triangular pyramid. It has three triangular faces meeting at the apex. There is a special case of a triangular pyramid called a tetrahedron, it has equilateral triangles for each of the faces. The following figure shows how a triangular pyramid looks like.
What Is Triangular Pyramid Formula?
A pyramid having a triangular base is called a triangular pyramid. It has three triangular faces meeting at the apex. Formulas for volume and surface area of the triangular pyramid are given below that are used in the triangular pyramid formula.
Volume= \(\dfrac{1}{3}\) × Base area ×Height
Surface Area = Base area + \(\dfrac{1}{2}\)(perimeter × slant height)
Let us see the applications of triangular pyramid formulas in the following solved examples.
Solved Examples Using Triangular Pyramid Formula

Example 1: Find the volume of a triangular pyramid having a base area of 10 \(cm^2\) and a height of 5 cm.
Solution:
To Find: Volume of the pyramid.
Given: base area = 10 \(cm^2\), height = 5 cm.
Using formula for volume of triangular pyramid
\(\text{Volume} =\dfrac{1}{3} \text{Base area} \times \text{Height}\)
= \(\dfrac{1}{3}(10 \times 5)\)
= 16.67 \(cm^3\)
Answer: The volume of the triangular pyramid is 16.67 \(cm^3\). 
Example 2: A triangular pyramid has a base area of 15 \(units^2\) and a sum of the lengths of the edges 60 units. Calculate the surface area of the triangular pyramid if the slant height is 20 units.
Solution:
To Find: Surface area of a triangular pyramid.
Given: Base area =15 \(units^2\), perimeter = 60 units.
Using the formula for surface area of triangular pyramid
\(\text{Surface Area} = \text{Base area} + \dfrac{1}{2} \text{perimeter} \times \text{slant height}\)
= \(15 + \dfrac{1}{2}(60 × 20)\)
= 15 + 600
= 615 \(units^2\)Answer: The surface area of the triangular pyramid is 615 \(units^2\)