How To Calculate The Volume Of A Triangular Prism: 6 Steps - WikiHow

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• Volume

How to Calculate the Volume of a Triangular Prism: Formulas & Examples Download Article Plus, how to find the area of a triangle when the height is unknown Co-authored by Grace Imson, MA and Dan Hickey

Last Updated: April 27, 2025 Fact Checked

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• Triangular Prism Volume Formula
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• Finding the Volume of a Triangular Prism
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• Finding Base Area without a Given Height
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• Properties of Triangular Prisms
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• Downloadable Practice Problems
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This article was co-authored by Grace Imson, MA and by wikiHow staff writer, Dan Hickey. Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University. There are 11 references cited in this article, which can be found at the bottom of the page. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 1,313,474 times.

Finding the volume of a triangular prism is easier than you might think. All you have to do is find the area of one of the triangular bases, then multiply it by the height of the prism! In this article, we’ll show you how to do just that, including how to find the area of the base whether the height is given or not. We’ll also review more properties of triangular prisms so you’re fully prepared for your next geometry exam.

Calculating Triangular Prism Volume Step by Step

1. Find the area of the triangular base with A r e a = 1 2 b h {\displaystyle Area={\frac {1}{2}}bh} .
2. Identify the height of the prism (the distance between the 2 triangular faces).
3. Enter the base area B {\displaystyle B} and the height H {\displaystyle H} into V o l u m e = B H {\displaystyle Volume=BH} .
4. Solve the equation to find the total volume of the triangular prism.

Steps

Section 1 of 4:

Formula for the Volume of a Triangular Prism

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1. Use the formula V = B H {\displaystyle V=BH} to find the volume of a triangular prism. According to physics teacher Joseph Quinones, “The volume of a triangular prism can be calculated by multiplying the base area of the triangle by the height of the prism.”[1] In this formula, V {\displaystyle V} is the total volume of the prism, B {\displaystyle B} is the area of one of the triangular bases, and H {\displaystyle H} is the height of the prism (the distance between the triangular bases, not the height of the triangular base itself).[2]
   • You may also see the equation written as V = ( 1 2 b h ) H {\displaystyle V=({\frac {1}{2}}bh)H} , where b {\displaystyle b} and h {\displaystyle h} represent the base and height of the triangular base. This is because 1 2 b h {\displaystyle {\frac {1}{2}}bh} is the formula for the area of a triangle.
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Section 2 of 4:

Finding the Volume of a Triangular Prism

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1. 1 Use A r e a = 1 2 b h {\displaystyle Area={\frac {1}{2}}bh} to find the area of the triangular base. Say the triangle has a base b {\displaystyle b} of 8 cm and a height h {\displaystyle h} of 9 cm. Just plug those values into A = 1 2 b h {\displaystyle A={\frac {1}{2}}bh} to find the area of the base:[3]
   • A = 1 2 ∗ 8 ∗ 9 = 36 {\displaystyle A={\frac {1}{2}}*8*9=36} . The area of the triangle is 36 cm 2.
   • Insert 36 for B {\displaystyle B} in the volume formula V = B H {\displaystyle V=BH} .
2. 2 Identify the height of the prism. Now you need to find the height of the triangular prism, which is the length of 1 of its sides (this is different from the height of the triangular base). For example, the prism may be 16 cm high. Place this number in the H {\displaystyle H} place of the formula V = B H {\displaystyle V=BH} .[4]
   • For example, your formula should now look like V = 36 ∗ 16 {\displaystyle V=36*16} .
3. 3 Multiply the base area by the height of the prism to find the volume. Since you now have all the parts of the equation, multiply the area of the triangular base by the height of the prism. The result will be the volume of the triangular prism.[5]
   • So, if V = 36 ∗ 16 {\displaystyle V=36*16} , the answer is 576 cm 3.
   • Remember that when finding volume, the answer will be in cubed units (and area is in square units).
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Section 3 of 4:

Finding the Area of the Base Triangle without a Given Height

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1. 1 Right triangle: Pythagorean Theorem A right triangle is a triangle where one angle equals 90° (a right angle); the side opposite the right angle is the hypotenuse and the other 2 sides are the legs (one is the base and one is the height, but they can be labeled interchangeably).[6] If you know the length of the hypotenuse ( c {\displaystyle c} ) and only one leg ( a {\displaystyle a} or b {\displaystyle b} ), plug those values into the Pythagorean Theorem (a2 + b2 = c2) to find the length of the missing leg:[7] Then, you can calculate the area of the triangle.[8]
   • Say the hypotenuse is 6 units and the base a {\displaystyle a} is 4 units:
     • 42 + b2 = 62
     • 16 + b2 = 36
     • b2 = 20
     • b = √20 (exact answer) or 4.472 (rounded answer).
   • Once you know the height, you can use A = 1 2 b h {\displaystyle A={\frac {1}{2}}bh} to find the triangle’s area:
     • A = ½*4*√20 = 2√20 (exact answer) or 8.944 (rounded answer)
2. 2 Isosceles triangle: A = ½[√(a2 - b2/4) x b] In this case, a {\displaystyle a} is the length of both equal sides and b {\displaystyle b} is the length of the third, unequal side.[9] So, let’s say the equal sides ( a {\displaystyle a} ) have a value of 4 and the base ( b {\displaystyle b} ) has a value of 2:
   • A = ½[√(42 - 22/4) x 2]
   • A = ½[√(16 - 4/4) x 2]
   • A = ½[√(16 - 1) x 2]
   • A = ½[√15 x 2]
   • A = √15 (exact answer) or 3.873 (rounded answer)
   • Alternate method: Divide your triangle in 2 vertically to form a right triangle ( a {\displaystyle a} becomes the hypotenuse and b / 2 {\displaystyle b/2} becomes one leg). Then, use the Pythagorean Theorem to solve for the height (the other leg).
3. 3 Equilateral triangle: A = (a2 x √3)/4 An equilateral triangle is a triangle where all sides are equal in length. To find the area (when the height is unknown), just plug in the length of one of the sides ( a {\displaystyle a} ) into the formula:[10] Say a {\displaystyle a} has a value of 6:
   • A = (62 x √3)/4
   • A = (36 x √3)/4
   • A = 9√3 (exact answer) or 15.588 (rounded answer)
4. 4 Scalene triangle: A = √s(s - a)(s - b)(s - c) This is known as Heron’s formula. In it, s {\displaystyle s} is half of the perimeter of the triangle (or (a+b+c)/2) and a {\displaystyle a} , b {\displaystyle b} , and c {\displaystyle c} are the lengths of the 3 sides.[11] So, let’s say you have a triangle with sides that measure 2, 3, and 4 units long:
   • First, find the value of s {\displaystyle s} :
     • s = (2 + 3 + 4)/2
     • s = 9/2 = 4.5
   • Then, plug in all values to find the area:
     • A = √4.5(4.5 - 2)(4.5 - 3)(4.5 - 4)
     • A = √4.5(2.5)(1.5)(0.5)
     • A = √4.5(2.5)(1.5)(0.5)
     • A = √4.5(1.875)
     • A = √8.4375 (exact answer) or 2.905 (rounded answer)
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Section 4 of 4:

Properties of Triangular Prisms

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1. Triangular prisms have 2 triangular bases and 3 parallelogram faces. Prisms are named for the shape of their base, so the base of any triangular prism is a triangle. The base has a congruent (same size and shape) and parallel face that is also a triangle at the other end of the prism. Since a triangle has 3 sides, that means it takes 3 more faces to fully enclose the prism. These faces are parallelograms (polygons with 2 sets of parallel sides, like rectangles or squares) that connect the triangles together. The base of each parallelogram is equal to the length of the triangle side it connects to, and the height of each parallelogram is the total height of the prism.[12]
   • Every cross-section of the prism parallel to the base will also be a congruent triangle.
   • Triangular prisms have 5 faces, 6 vertices, and 9 edges.
   • A triangular prism is also known as a pentahedron because it has 5 faces (penta means 5).

Triangular Prism Volume Calculator, Practice Problems, and Answers

Sample Triangular Prism Volume Calculator Sample Calculating Triangular Prism Volume Practice Problems Sample Calculating Triangular Prism Volume Answers

Expert Q&A

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• Question How do I find the volume of other 3D shapes like a cylinder? Grace Imson, MA Math Teacher Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University. Grace Imson, MA Math Teacher Expert Answer To find the volume of a cylinder, first find the area of the circular surface, which is Pi times the radius squared, then multiply that by the height of the cylinder. Thanks! We're glad this was helpful. Thank you for your feedback. If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow Yes No Not Helpful 0 Helpful 1
• Question How do I get the volume of a triangular prism? Joseph Quinones Physics Teacher Joseph Quinones is a Physics Teacher working at South Bronx Community Charter High School. Joseph specializes in astronomy and astrophysics and is interested in science education and science outreach, currently practicing ways to make physics accessible to more students with the goal of bringing more students of color into the STEM fields. He has experience working on Astrophysics research projects at the Museum of Natural History (AMNH). Joseph recieved his Bachelor's degree in Physics from Lehman College and his Masters in Physics Education from City College of New York (CCNY). He is also a member of a network called New York City Men Teach. Joseph Quinones Physics Teacher Expert Answer To calculate the volume of a triangular prism, you need to multiply the base area of the triangle by the height of the prism. Thanks! We're glad this was helpful. Thank you for your feedback. If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow Yes No Not Helpful 0 Helpful 1
• Question How do I calculate the area of a triangular prism? Community Answer To find the surface area of a triangular prism, you would find the area of all the faces, then add them together. Thanks! We're glad this was helpful. Thank you for your feedback. If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow Yes No Not Helpful 272 Helpful 341

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Tips

• Ensure that the units of measurement are the same for all parts of the triangular prism before you begin the calculation. For example, if 1 part of the prism is in millimeters and the rest is in centimeters, convert the millimeters to centimeters first. Thanks Helpful 1 Not Helpful 0
• The formula V = B H {\displaystyle V=BH} can be used to find the volume of any prism. Thanks Helpful 0 Not Helpful 1

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Expert Interview

Thanks for reading our article! If you’d like to learn more about physics, check out our in-depth interview with Joseph Quinones.

References

1. ↑ Joseph Quinones. Physics Teacher. Expert Interview
2. ↑ https://flexbooks.ck12.org/cbook/interactive-math-7-flexlet/section/4.6/related/lesson/volume-of-triangular-prisms-msm7/
3. ↑ https://flexbooks.ck12.org/cbook/ck-12-cbse-maths-class-6/section/13.6/primary/lesson/area-of-triangle/
4. ↑ https://www.ck12.org/geometry/volume-of-triangular-prisms/lesson/Volume-of-Triangular-Prisms-MSM7/
5. ↑ https://flexbooks.ck12.org/cbook/ck-12-interactive-middle-school-math-7-for-ccss/section/6.10/related/lesson/volume-of-triangular-prisms-msm7/
6. ↑ https://www.palmbeachstate.edu/prepmathlw/Documents/the_pythagorean_theorem.pdf
7. ↑ https://www.palmbeachstate.edu/prepmathlw/Documents/the_pythagorean_theorem.pdf
8. ↑ https://content.byui.edu/file/b8b83119-9acc-4a7b-bc84-efacf9043998/1/Math-2-4-6.html
9. ↑ https://www.cuemath.com/measurement/area-of-an-isosceles-triangle/

More References (3)

10. ↑ https://www.omnicalculator.com/math/equilateral-triangle
11. ↑ https://www.cuemath.com/measurement/area-of-scalene-triangle/
12. ↑ https://amsi.org.au/ESA_middle_years/Year6/Year6_2cT/Year6_2cT_R1_pg3.html

About This Article

Co-authored by: Grace Imson, MA Math Teacher This article was co-authored by Grace Imson, MA and by wikiHow staff writer, Dan Hickey. Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University. This article has been viewed 1,313,474 times. 34 votes - 67% Co-authors: 71 Updated: April 27, 2025 Views: 1,313,474 Categories: Volume Article SummaryX

To calculate the volume of a triangular prism, first you need to find the area of one of the triangular bases by multiplying ½ by the base of the triangle and by the height of the triangle. For example, if the base is 8 and the height is 9, you would get ½ x 8 x 9 = 36. Therefore, the area is 36. Next, plug the area into the formula for finding the volume of a triangular prism, which is V = b x h, or volume equals the area of the base multiplied by the height of the prism. Now, plug the height of the prism into the formula and solve. As an example, if the area of the triangular base is 36 and the height of the prism is 16, you would get 36 x 16 = 576. Therefore, the volume of the triangular prism is 576. Write your answer in cubic units. If you want to learn how to calculate the height of a regular triangle, keep reading! Did this summary help you?YesNo

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