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A triangular prism is a three-dimensional shape that consists of a triangular base and three rectangular faces. Calculating its volume is essential in geometry and engineering, as it helps in determining the amount of space it occupies or the capacity of a container. To accurately calculate the volume of a triangular prism, one must understand the relationships between its base, height, and length. Through this calculation, individuals can confidently determine the volume of any triangular prism, enabling them to make informed decisions in various real-world applications. This article will explore the step-by-step process of calculating the volume of a triangular prism, accompanied by examples and practical information to enhance understanding and application. Through mastering this mathematical concept, readers will be equipped with a valuable skill that can be applied in a range of professions, such as architecture, construction, or even everyday problem-solving.

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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 is a relatively straightforward process that involves finding the area of the base triangle and multiplying it by the height of the prism. By following the steps outlined above, you can confidently determine the volume of any triangular prism. It is important to remember that the formula for volume works for any triangular prism, regardless of the size or shape of the triangular base. Regular practice and familiarity with the formula will help in efficiently calculating the volume of triangular prisms and applying this knowledge to real-life scenarios.

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