Triangular Pyramid Formulas | List of Triangular Pyramid Formulas You Should Know - BYJUS

# Triangular Pyramid Formulas

The great pyramids of Egypt are the most popular real life examples of the shape of a three dimensional pyramid. A pyramid is a 3D shape with a base shaped like a polygon. In this article we will learn the formulas to calculate the surface area and the volume of a triangular pyramid....Read MoreRead Less

### Formulas Related to the Triangular Pyramid

A triangular pyramid is a solid shape with a triangular base and three triangular lateral faces. The lateral faces meet at a common point known as the apex of the pyramid.

A triangular pyramid has two main formulas – one used to calculate the surface area and the other used to calculate its volume.

A triangular pyramid as a solid shape is as shown in the image. ### Formula for the Surface Area of a Triangular Pyramid

The surface area of a pyramid is the sum of the areas of all its lateral faces and the base. A triangular pyramid has 3 lateral faces and 1 base, all triangular in shape. So its total surface area is given by:

Total surface area = Lateral surface area + Base surface area

Here the lateral surface area is the sum of the areas of the three triangular lateral faces.

Surface area is always measured in square units.

### Formula for the Volume of a Triangular Pyramid

Volume of a triangular pyramid is the measure of the space enclosed within the faces of the pyramid.

Volume of a triangular pyramid, V = $$\left(\frac{1}{3}\right)$$ × Base Area × h

In which,

• Base area is the area of the triangular base
• ‘h’ is the height of the pyramid. It is the perpendicular distance from the apex to the base.

Volume is measured in cubic units such as $$m^3,cm^3$$,and  $$in^3$$.

### Solved Examples

Example 1: What is the volume of a triangular pyramid which has a base area of 4 $$cm^2$$ and the height is 5 centimeters?

Solution:

Details in the question,

Base area = 4 $$cm^2$$

Height = 5 centimeters

V= $$\frac{1}{3}$$ × Base Area × Height        Formula for the volume of a triangular pyramid

Substituting the values:

V = $$\frac{1}{3}$$ × 4 × 5

V = 6.67        Simplify

Hence, the volume of the given triangular pyramid is 6.67 $$cm^3$$.

Example 2: Joe made a triangular pyramid with sand near the ocean. Its volume is 610 $$cm^3$$ and the base area is 61 square centimeters. What is the height of the triangular pyramid?

Solution:

Given data, base area = 61 $$cm^2$$

Volume = 610 $$cm^3$$

V= $$\frac{1}{3}$$ × Base Area × Height       Formula for the volume of a triangular pyramid

Substituting the given values:

We get, $$\frac{1}{3}$$ × 61 × h = 610

Solving for h,

h = $$\frac{610\times 3}{61}$$

h = 30   [Simplify]

Hence, the height of the triangular pyramid is 30 cm.

Example 3:

Determine the surface area of the triangular pyramid given in the diagram. Solution:

To determine the surface area of the given pyramid let us draw its net: Area of the base: $$\frac{1}{2}$$ × 9 × 6 = 27

Area of the lateral face: $$\frac{1}{2}$$ × 9 × 11 = 49.5

The surface area of the triangular pyramid = Areas of the lateral faces + Area of the base

= 27 + 49.5 + 49.5 + 49.5    [There are three identical lateral faces]

= 175.5

Therefore, the surface area of the triangular pyramid is 175.5 square inches.