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A triangular prism is a three-dimensional geometric shape that consists of two triangular bases and three rectangular faces. Calculating its volume is essential in various fields such as architecture, engineering, and construction. By determining the volume of a triangular prism, one can accurately estimate the required materials, plan and design structures, and ensure their stability. This guide will provide a step-by-step explanation of how to calculate the volume of a triangular prism, allowing readers to grasp the concepts and apply them to real-world scenarios effectively.

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Calculating the volume of a triangular prism is often easily assumed to be the same as calculating the volume of a pyramid. However, a triangular prism is a three-sided polyhedron with two triangular parallel bases and three rectangular faces. To calculate the volume of a triangular prism, you simply find the area of one of the bases of the triangle and multiply it by the height of the prism.

## Steps

### Find the area of triangle

**Find the height and length of the base of a triangle.**Look at the triangle and write down the length of its base and its height. For example, your triangle has a base side of 8 cm and a height of 9 cm.

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- Remember that you are specifying the height of
*the triangle*, not the height of the prism. - You can use either triangle of the base of the prism since they are the same size.

**Substitute the numbers into the formula to find the area of a triangle.**Once you know the length of the base and the height of the triangle, you will substitute these numbers into the formula to calculate the area of the triangle:

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- Area = 1/2 x base length x height. You can also see the formula written as DRAW=first2bH{displaystyle V={frac {1}{2}}bh}

**Multiply 1/2 by the length of the base and multiply by the height to calculate the area of the triangle.**To find the area of the base triangle of the prism, you would multiply the length of the base by the height and multiply by 1/2. Remember to write your results in squared units because you are calculating area.

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- For example, if the base length is 8 and the height is 9, your calculation would be DRAW=first2∗8∗9{displaystyle V={frac {1}{2}}*8*9} . The area of the triangle is 36 cm
^{2}.

### Find the volume of the prism

**Substitute the area value of the triangle into the formula to find the volume of the prism.**The area of the triangle is one of two numbers you need to find the volume of the prism. In the formula DRAW=bH{displaystyle V=bh} , the area of the triangle is DRAW=b{displaystyle V=b} .

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- For the example above, the formula would be DRAW=36∗H{displaystyle V=36*h} .

**Determine the height of the prism and substitute the formula.**Now you need to find the height of the triangular prism, i.e. the length of one of the sides. For example, a prism has a height of 16 cm. You would substitute this number in the formula DRAW=H{displaystyle V=h} .

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- For example, your calculation will now be DRAW=36∗16{displaystyle V=36*16} .

**Multiply the area of the triangle by the height of the prism to find the volume.**Since you now have all the components of the equation, you will multiply the area of the base of the triangle by the height of the prism. The result will be the volume of the triangular prism.

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- Thus, if DRAW=36∗16{displaystyle V=36*16} , the answer would be 576 cm
^{3}.

## Advice

- Be sure to use the same unit of measure for all prismatic measurements before calculating. For example, if some measurements of a prism are in millimeters and the rest are in centimeters, you need to convert millimeters to centimeters first.

This article is co-authored by a team of editors and trained researchers who confirm the accuracy and completeness of the article.

The wikiHow Content Management team carefully monitors the work of editors to ensure that every article is up to a high standard of quality.

This entry has been viewed 219,232 times.

Calculating the volume of a triangular prism is often easily assumed to be the same as calculating the volume of a pyramid. However, a triangular prism is a three-sided polyhedron with two triangular parallel bases and three rectangular faces. To calculate the volume of a triangular prism, you simply find the area of one of the bases of the triangle and multiply it by the height of the prism.

In conclusion, calculating the volume of a triangular prism involves a straightforward process that requires the knowledge of the prism’s base and height. By multiplying the base area with the prism’s height, one can determine the volume. This equation is applicable for all types of triangular prisms, making it a useful tool for various geometric calculations. Understanding how to calculate the volume of a triangular prism is essential for students, architects, engineers, and anyone working with three-dimensional shapes. Overall, this formula provides a reliable and efficient method for determining the volume of a triangular prism and contributes to a deeper understanding of geometry and spatial reasoning.

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