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

Skip to ContentQuizzes

• PRO Courses Guides New Tech Help Pro Expert Videos About wikiHow Pro Upgrade Sign In
• QUIZZES
• EDIT Edit this Article
• EXPLORE Tech Help ProAbout UsRandom ArticleQuizzes Request a New ArticleCommunity DashboardThis Or That GameForums Popular Categories Arts and EntertainmentArtworkBooksMoviesComputers and ElectronicsComputersPhone SkillsTechnology HacksHealthMen's HealthMental HealthWomen's HealthRelationshipsDatingLoveRelationship Issues Hobbies and CraftsCraftsDrawingGamesEducation & CommunicationCommunication SkillsPersonal DevelopmentStudyingPersonal Care and StyleFashionHair CarePersonal HygieneYouthPersonal CareSchool StuffDating All Categories Arts and EntertainmentFinance and BusinessHome and GardenRelationship Quizzes Cars & Other VehiclesFood and EntertainingPersonal Care and StyleSports and Fitness Computers and ElectronicsHealthPets and AnimalsTravel Education & CommunicationHobbies and CraftsPhilosophy and ReligionWork World Family LifeHolidays and TraditionsRelationshipsYouth
• LOG IN

  Log in

  Social login does not work in incognito and private browsers. Please log in with your username or email to continue. Facebook Google wikiHow Account No account yet? Create an account
• RANDOM

• Home
• Random
• Browse Articles
• Learn Something New
• QuizzesHot
• Forums
• Courses
• Happiness Hub
• Play Games
• This Or That Game
• Train Your Brain
• Explore More
• Support wikiHow
• About wikiHow

• Log in / Sign up

Terms of Use wikiHow is where trusted research and expert knowledge come together. Learn why people trust wikiHow

• Categories
• Education and Communications
• Studying
• Mathematics
• Geometry
• Calculating Volume and Area
• 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: October 24, 2024 Fact Checked

Download Article

• Triangular Prism Volume Formula
|
• Finding the Volume of a Triangular Prism
|
• Finding Base Area without a Given Height
|
• Properties of Triangular Prisms
|
• Downloadable Practice Problems
|
• Video
|
• Expert Interview
|
• Q&A
|
• Tips

|Show more |Show less ARTICLE VIDEO X

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 10 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 1,295,947 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

Download Article

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.” 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).[1]
   • 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.
Advertisement

Section 2 of 4:

Finding the Volume of a Triangular Prism

Download Article

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:[2]
   • 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} .[3]
   • 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.[4]
   • 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).
Advertisement

Section 3 of 4:

Finding the Area of the Base Triangle without a Given Height

Download Article

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).[5] 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:[6] Then, you can calculate the area of the triangle.[7]
   • 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.[8] 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:[9] 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.[10] 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)
Advertisement

Section 4 of 4:

Properties of Triangular Prisms

Download Article

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.[11]
   • 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

Community Q&A

Search Add New Question

• 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 271 Helpful 341
• Question How can I find the volume of a rectangular prism? Community Answer To find the volume of a rectangular prism, multiply the prism's width, height, and length. V = w*h*l 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 184 Helpful 230
• Question How do I find the volume of a square pyramid? Donagan Top Answerer V = (1/3)(s²)(h), where s is the length of a side of the base, and h is the height. 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 157 Helpful 97

See more answers Ask a Question 200 characters left Include your email address to get a message when this question is answered. Submit Advertisement

Video

Read Video Transcript

Tips

• The formula V = B H {\displaystyle V=BH} can be used to find the volume of any prism. Thanks Helpful 0 Not Helpful 0
• 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 0 Not Helpful 0

Submit a Tip All tip submissions are carefully reviewed before being published Name Please provide your name and last initial Submit Thanks for submitting a tip for review! Advertisement

You Might Also Like

How toCalculate the Volume of a Pyramid How toCalculate the Area of a Triangle How toCalculate the Volume of a Cylinder How toCalculate the Volume of a Sphere How to Find the Volume of Basic Shapes How to Find the Volume of a Cube from a Side, Surface Area, or Diagonals How to Calculate the Volume of a Rectangular Prism How toCalculate CBM How toCalculate Volume of a Box How toCalculate the Volume of an Irregular Object How to Find the Volume of a Cone How toFind Density How toCalculate the Volume of a Prism How toDetermine Cubic Yards Advertisement

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

More References (2)

10. ↑ https://www.cuemath.com/measurement/area-of-scalene-triangle/
11. ↑ 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 1,295,947 times. How helpful is this? Co-authors: 70 Updated: October 24, 2024 Views: 1,295,947 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

In other languages Spanish Portuguese Italian German Russian French Chinese Dutch Indonesian Thai Arabic Hindi Vietnamese Korean Japanese

• Print
• Send fan mail to authors

Thanks to all authors for creating a page that has been read 1,295,947 times.

Reader Success Stories

• 

  Parkna Rey

  Mar 24, 2017

  "I had to study for a test on volume and surface area. I wasn't very good at both, so I asked my sister. She..." more

More reader stories Hide reader stories Share your story

Did this article help you?

Yes No Advertisement Cookies make wikiHow better. By continuing to use our site, you agree to our cookie policy. Co-authored by: Grace Imson, MA Math Teacher Click a star to vote % of people told us that this article helped them. Co-authors: 70 Updated: October 24, 2024 Views: 1,295,947

Parkna Rey

Mar 24, 2017

"I had to study for a test on volume and surface area. I wasn't very good at both, so I asked my sister. She..." more

Paula Barrows

Mar 8, 2016

"When my son is having trouble understanding the formula to a math problem, inevitably he will understand the..." more

Anonymous

Mar 1, 2017

"I had a math project and needed to find the volume formula of a triangular prism. I searched numerous websites but..." more

D. P.

Feb 24, 2022

"I really needed the formula for my math homework and I didn't know what it was. Other websites gave long..." more Rated this article:

Ashraful Alam

Feb 28, 2017

"I am a 6th grader. My mom told me to study for the upcoming state test, so I practiced in a book. The book had some..." more Share yours! More success stories Hide success stories

Quizzes

Do I Have a Dirty Mind QuizTake QuizAm I a Good Kisser QuizTake QuizRizz Game: Test Your RizzTake QuizWhat's Your Red Flag QuizTake QuizAm I Smart QuizTake QuizHow Insecure Am I QuizTake Quiz

You Might Also Like

How toCalculate the Volume of a PyramidHow toCalculate the Area of a TriangleHow toCalculate the Volume of a CylinderHow toCalculate the Volume of a Sphere

Featured Articles

How toGet Six Pack Abs FastHow toImprove Your Personality18 Best Strategies to Get Out of Your Comfort ZoneHow toMake Your Mascara Look GreatHow toTransform Yourself for the New YearHow toWrite a Book

Trending Articles

How to Wrap a Box Like a ProHow toCelebrate HanukkahHow toDo Simple and Cute HairstylesHow toGet Into the Spirit of Christmas when You Don't Feel It Any MoreWhat Does the Thumbs Up 👍 Emoji Mean & Why Is It So Controversial?How to Make Your Girlfriend Fall For You Again (And Keep Her for Good!)

Featured Articles

How toHave a Glow UpThe Correct Way to Do Push-Ups for BeginnersHow toFeng Shui Your BedroomAm I In Love QuizHow & Where to Apply Perfume (Plus, Common Mistakes to Avoid)How toKnow if You Are Ready for a Relationship

Featured Articles

How toDevelop a Thick SkinHow toCelebrate HanukkahHow toTell if a Diamond is RealWhich Hogwarts House Do I Belong In QuizWhat to Do When You Get a Gift You Don't LikeWhat Kind of Reality Check Do I Need Quiz

Watch Articles

How toThicken SyrupHow toStraighten Your HairHow toClean Metal JewelryHow toSeason Chicken3 Unique Ways to Re-Invent the Neckline of a ShirtHow toMoisturize Your Face Naturally

Trending Articles

How toTell When a Guy is No Longer Interested in YouHow toCelebrate KwanzaaWhat Does “Much Appreciated” Mean? Plus, Alternatives for Business EmailsHow to Trim, Slice, & Cut the Perfect BrisketHow toFeel More AttractiveHow toMake Your Mascara Look Great

Quizzes

What Disney Princess Am I QuizTake QuizDo I Have a Phobia QuizTake QuizGuess My Age QuizTake QuizAm I a Genius QuizTake QuizDepression TestTake QuizWhat Human Emotion Am I QuizTake Quiz

• Categories
• Education and Communications
• Studying
• Mathematics
• Geometry
• Calculating Volume and Area
• Volume

wikiHow Newsletter You're all set! Helpful how-tos delivered toyour inbox every week! Sign me up! By signing up you are agreeing to receive emails according to our privacy policy.

• Home
• About wikiHow
• Experts
• Jobs
• Contact Us
• Site Map
• Terms of Use
• Privacy Policy
• Do Not Sell or Share My Info
• Not Selling Info
• Contribute

Follow Us

×

wikiHow Tech Help Pro:

Develop the tech skills you need for work and life

Let's do this! X --3553