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Three Ways to Find the Volume of Pyramids

The volume of a pyramid is the number of cubic units inside the pyramid.

Before we go over calculating this volume, let’s review what a pyramid is. A pyramid is a three-dimensional figure where the base of the pyramid is connected to its point (or vertex) by triangular faces. Each of these triangles is called a lateral face, and the distance from the vertex of the pyramid to the base is considered to be the pyramid's height.

How Do You Find the Volume of a Pyramids?

Here is the pyramid volume formula:

Volume of pyramid formula

In this formula, Ab = the area of the base and h = height of the pyramid. The volume of the pyramid is dependent on what type of polygonal base the pyramid has. So in order to find the right pyramid volume, let's dive into the different formulas for each of these pyramid types.

How to Find the Volume of a Triangular Pyramid

Triangular pyramids, otherwise known as polyhedrons, have three triangular faces whose perpendicular height intersects the triangular base. The formula for a triangle pyramid is:

volume of pyramid: Formula for a triangle pyramid

The slant height of a pyramid is simply its perpendicular height, which is labeled in the figure below:

volume of pyramid: Image that shows the slant height of a pyramid

When you're dealing with a pyramid that has an equilateral triangle base, you can use the following formula:

volume of pyramid

Let's use this formula to solve for the volume of the following triangle:

volume of pyramid: Formula for equilateral triangle base pyramid

volume of pyramid: Image that shows equilateral triangle base pyramid

volume of pyramid: Equation of an equilateral triangle base pyramid

volume of pyramid: Equation of an equilateral triangle base pyramid

volume of pyramid: Equation of an equilateral triangle base pyramid

Equation of an equilateral triangle base pyramid

Equation of an equilateral triangle base pyramid

How to Find the Volume of a Square Pyramid

To determine the volume of a square-based pyramid or rectangular pyramid, you will use the following equation:

Formula for determining the volume of a square-based or rectangular pyramid

For both rectangular bases and square bases, the area of the base is simply the two side lengths multiplied together. Let's determine the volume of the figure below:

Image that shows how to determine the volume of a square-based or rectangular pyramid

Equation of how to determine the volume of a square-based or rectangular pyramid

Equation of how to determine the volume of a square-based or rectangular pyramid

Equation of how to determine the volume of a square-based or rectangular pyramid

Equation of how to determine the volume of a square-based or rectangular pyramid

How to Work With the Volume of Pyramids

It's important to know how to solve for the volume for different types of pyramids. Whether a pyramid has a triangular, rectangular, or square base determines what type of volume formula you’ll use. Once you've mastered these pyramid types, you'll be able to move onto the volume of a cone or pentagonal pyramid.

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