How to Calculate the Volume of a Pyramid

To calculate the volume of a pyramid, simply find the product of the area of the base times the height of the pyramid, then multiply the result by 1/3. This calculation method will vary slightly, depending on whether the base of the pyramid is a triangle or a rectangle. Follow the steps below to calculate the area of the pyramid.

Table of Contents

Pyramid with Rectangular Base

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Find the length and width of the bottom. In this example, the length of the bottom is 4 cm and the width is 3 cm. For squares, the calculation is similar, but the width and length will then be equal. Write these values down on paper.

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Multiply the length by the width to calculate the area of the base. To calculate the area of the base of the apex, we only need to take 3 cm x 4 cm = 12 cm ²^{[1] X Research Source}

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Multiply the area of the base by the height. The base area calculated above is 12 cm ² and the height is 4 cm, you just need to take 12 cm ² times 4 cm. 12 cm ² x 4 cm = 48 cm ³

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Divide the result we just calculated by 3. Instead of dividing, we can multiply the result by 1/3, both ways are the same. 48 cm ³ /3 = 16 cm ³ . The volume of a pyramid of height 4 cm with a rectangular base with side lengths 4 cm and 3 cm would be 16 cm ³ . Remember to record results in volume units when you work with three-dimensional space.

Pyramid with Triangle Base

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Find the length and width of the bottom. The length and width in this case must be perpendicular to each other, or we can also think of them as the base and height of the base of the triangle. In this example, the width of the triangle is 2 cm and the length is 4 cm. Write the values down on paper. ^{[2] X Research Source}

If the length and width are not perpendicular and you do not know the height of the triangle, you can use other methods to calculate the area of the triangle.

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Calculate the area of the bottom. To calculate the area of the base, we just need to substitute the measured values of the base and the height of the triangle into the following formula: A = 1/2(b)(h). The specific calculation is as follows:

A = 1/2(b)(h)
A = 1/2(2)(4)
A = 1/2(8)
A = 4 cm ²

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Multiply the area of the base by the height of the pyramid. The base area calculated above is 4 cm ² and the height is 5 cm. 4 cm ² x 5 cm = 20 cm ³ .

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Divide the result just calculated by 3. 20 cm ³ /3 = 6.67 cm ³ . Therefore, the volume of a pyramid of height 5 cm with the base of a triangle with the lengths of the perpendicular sides 2 and 4 cm will be 6.67 cm. ³

Advice

In a square pyramid, the height, the birth line and the base side obey the Pythagorean theorem as follows: (bottom edge ÷ 2) ² + (height) ² = (birth line) ²
This method can be generalized to objects such as pentagonal pyramids, hexagonal pyramids, etc. The general procedure for calculation is as follows: A) calculate the area of the base; B) measure the height from the top of the pyramid to the center of the base; C) multiply A by B; D) divide the result just calculated by 3.
In an “regular” pyramid, the generation, base and side lines obey the Pythagorean theorem as follows: (bottom edge ÷ 2) ² + (generate) ² = (side) ²

Warning

The pyramid has three types of heights: the birth line is directed from the apex and is perpendicular to the base edge; the actual height is directed from the top of the tip to the center of the base, i.e. perpendicular to the base; The length of the lateral side is one side of the lateral triangle, connecting the apex to the base. To calculate the volume you MUST use the “real” height.

Steps

Pyramid with Rectangular Base

Pyramid with Triangle Base

Advice

Warning

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