# Volumne of a Pyramid

How to find the volume of a pyramid: formula, examples, and their solutions.

## Formula

*V* = (1/3)*Bh**V*: Volume of a pyramid*B*: Base area*h*: Height of the pyramid

This formula can be used in any pyramid.

(not only a regular pyramid)

## Example 1

The base is a rectangle.

Its sides are 7 and 4.

So *B* = 28.

Area of a rectangle

The height of the given pyramid is 9.

*B* = 28*h* = 9

So *V* = (1/3)⋅28⋅9.

Cancel the denominator 3

and reduce 9 to 3.

28⋅3 = 84

So *V* = 84.

## Example 2

The three right triangle faces are

all perpendicular to each other.

So set one of these faces as the base.

Set the bottom face as the base.

The base is a right triangle.

Its legs are 8 and 9.

So *B* = (1/2)⋅8⋅9.

Area of a triangle

(1/2)⋅8 = 4

4⋅9 = 36

So *B* = 36.

The blue edge is perpendicular to the base.

So the blue edge is the height.

So *h* = 10.

*B* = 36*h* = 10

So *V* = (1/3)⋅36⋅10.

(1/3)⋅36 = 12

12⋅10 = 120

So *V* = 120.