How to Calculate the Volume of a Pyramid: 8 Steps

2024 Author: Samantha Chapman | [email protected]. Last modified: 2023-12-17 09:13

To calculate the volume of a pyramid, all you have to do is multiply the area of the base by its height and take a third of it. The method may vary slightly depending on whether the base is triangular or rectangular. If you want to know how to perform this calculation, simply follow the steps illustrated in this article.

Steps

Method 1 of 2: Rectangular Pyramid Base

Step 1. Find the length and width of the base

In this example, the base length is 4cm, while the width value is 3cm. In case you have a square base, the method will be the same; the only thing that changes is obviously the fact that length and width will have the same value. Then write down these measurements.

Step 2. Multiply the length by the width value to find the base area

To calculate the area of the base, simply do the following multiplication 3cm x 4cm = 12cm².

Step 3. Multiply the area of the base by the height

The base area is 12 cm², while the height is 4 cm, so you just have to do this further multiplication: 12 cm² x 4 cm = 48 cm³.

Step 4. Divide the final result by 3

We will therefore have 48 cm³/ 3 = 16 cm³. At this point we can say that the area of a pyramid with a height of 4 cm and with a rectangular base having a width and length of 3 cm and 4 cm respectively, will be equal to 16 cm³. Always remember to express the value in cubic units whenever you are dealing with three-dimensional spaces.

Method 2 of 2: Triangular Base Pyramid

Step 1. Find base and base height

Let's consider a right triangle, in which the two legs can be considered the base and the height. In this example, the height of the triangle is 2cm, while the base has a value of 4cm. Then write down these measurements.

In case you do not have the two sides of a right triangle, there are several methods to try to calculate the area of a triangle

Step 2. Calculate the area of the base

To get the area of the base, simply relate the base and the height of the triangle in the following formula: A = 1/2 (b) (h).

Here's how to do it:

• A = 1/2 (b) (h)
• A = 1/2 (2) (4)
• A = 1/2 (8)
• A = 4 cm²

Step 3. Multiply the area of the base by the height of the pyramid

At this point we know that the base area is 4 cm², while the height of the pyramid is 5 cm. We will therefore have: 4 cm² x 5 cm = 20 cm³.

Step 4. Divide the result by 3

20 cm³/ 3 = 6.67 cm³. Therefore, the volume of a 5 cm high pyramid with a triangular base 2 cm high and 4 cm base will have a value equal to 6.67 cm³.

Advice

• In all regular pyramids, the lateral height, the height of the pyramid and the apothem are related by the Pythagorean theorem: (apothem)² + (height)² = (side height)²
• This method can also be applied to pyramids with a pentagonal, hexagonal base, etc. The general method is: A) calculate the area of the base; B) measure the height of the pyramid or that which goes from the vertex to the center of the figure of the base; C) multiply A by B; D) divide by 3.
• Also in the square-based pyramid the lateral height, the height of the pyramid and the apothem are linked by the Pythagorean theorem: (base apothem)² + (height)² = (side height)²