Volume of a Triangular Prism Calculator
Our volume of a triangular prism calculator is a simple tool that can solve all your queries connected to the topic - using one of the 6 available methods with 6 different sets of data. 📐
Take a look at our article below - you will not only discover what the formula is for the volume of a triangular prism, we will also explain the mathematical laws that make it possible.
Get ready - we'll help you finally understand how to find the volume of a triangular prism all by yourself. 🤓
What is a triangular prism?
A triangular prism is a solid that is formed by wrapping two parallelly faced triangles as top and bottom faces. A triangular prism is a polyhedron with triangles as bases and rectangles as lateral faces.
How to use the volume of a triangular prism calculator?
So, how do you find the volume of a triangular prism with the help of our tool? It's as easy as it seems - you're just seconds away from your result!
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Select the type of triangle face calculation
Think about what you already know about the triangle present in the prism, and find out which values are given:
- ▲ Base and height - you already know the length of the base and the triangle's height;
- ◣ Right triangle - your triangle has a right angle (90°) between two of its arms. You know the lengths of these arms (this option serves as the volume of a right triangular prism calculator);
- ▲ 3 sides - you know the lengths of all three sides of the triangle;
- ▲ 2 sides + angle between - you know the lengths of two sides and the value of the angle between them;
- ▲ 2 angles + side between - you know the value of two angles of the triangle and the length of the side that lies between them; and
- ▲ Area of triangular face - the perfect option if you're one step ahead and you have already calculated the area of a triangular face of your prism.
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Enter all the data given in your query
You can choose from 11 different units - don't hesitate to mix them!
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Your results are here 🎉
It was that bad, was it? How about trying our other prism calculators:
🔺 Triangular:
♦️ Rectangular:
How to calculate the volume of a triangular prism?
As we've already mentioned, there are 6 ways to find out what is the volume of a triangular prism in our calculator. Let's quickly browse all of them.
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▲ Base and height
This is the basic volume equation of a triangular prism:
Volume = 0.5 * Base * Height * Length
Where:
- Base and Height are the values of the triangular face of the prism; and
- Length means the length of the entire prism, i.e., the distance between two faces.
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◣ Right triangle
Probably the most popular type of prism!
The right triangular prism formula looks as follows:
Volume = Length * ((a * b) / 2)
Where:
- a and b are the sides of the triangle that touch the right angle; and
- Length means the length of the entire prism, i.e., distance between two faces.
In order to calculate the c side, use the Pythagorean theorem.
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▲ 3 sides
Volume = 0.25 * √( (a+b+c) * (-a+b+c) * (a-b+c) * (a+b-c) ) * Length
Where:
- √ - means the square root of all the multiplied sums of the triangle sides (x² = y, √y = x);
- a, b, and c are sides of the triangular face; and
- Length means the length of the entire prism, i.e., distance between two faces.
💡 Remember that for three lines to form a triangle, the sum of lengths of any two sides must be greater than the length of the third side!
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▲ 2 sides + angle between
Volume = 0.5 * a * b * sin(Angle γ) * Length
Where:
- sin - sine of the Angle γ (use the law of sines calculator to understand the basis of this equation); and our
- a and b are the sides of the triangle that touch the Angle γ;
- Angle γ - its value must be between 0 and 180 degrees; and
- Length means the length of the entire prism, i.e., distance between two faces
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▲ 2 angles + side between
Volume = 0.5 * a *((a * sin(Angle β))/ sin(Angle β + Angle γ)) * sin(Angle γ) * Length
Where:
- sin - sine of a given angle. Found with the sines tables, based on the law of sines (as mentioned above);
- a is the side of a triangle that touches both Angle γ and Angle β;
- Angle γ - its value must be between 0 and 180 degrees;
- Angle β - its value must be between 0 and 180 degrees; and
- Length means the length of the entire prism, i.e., distance between two faces
💡 The sum of Angle γ and Angle β also can't exceed 180 degrees (Angle β + Angle γ < 180°).
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▲ Area of triangular face
The best solution if you already know the triangular face.
Volume = Triangle base area * Length
Where:
- Triangle base area is given in area unit e.g., square inches (in²), square meters (m²), or square miles (mi²); and
- Length means the length of the entire prism, i.e., distance between two faces
FAQ
What are the 5 faces of a triangular prism?
The two triangular faces are bases of a prism. The three rectangular faces are lateral faces. Consequently, each triangular prism has 9 edges and 6 vertices.
What is the volume of a triangular prism with base 10 and length 10?
The answer is 100. This is because the volume is the product of base area and prims's length. Remember about the units: if your base area is in cm²
and length in cm
, then your answer is in cm³
. If the units are inconsistent, remember to apply the formula only after rewriting the data into consistent units!
How do I calculate the volume of a triangular prism given sides?
If you know the sides of a triangular prism and need to compute its volume, follow these steps:
- Let's agree that
a, b, and c
stand for the sides of the triangle that is the base of our prism, andL
is the prism's length. - Compute the area of the base by applying Heron's formula
Area = 0.25*√((a+b+c) * (-a+b+c) * (a-b+c) * (a+b-c))
- Multiply the result from Step 2. by the prism's length
L
. - That's it! You've got the volume of your prism.
