The Volume Of A Triangular Prism Calculator
A triangular prism is a length of constant triangular cross-section. Its volume is the area of that triangle times the length, and the triangular face comes from Heron's formula when you only know the three sides.
Volume
60
- Triangle face area
- 6
- Lateral area
- 120
- Total surface area
- 132
- Perimeter of the triangle
- 12
Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.
The formula this calculator uses
volume = triangle area x length, where triangle area = sqrt(s(s-a)(s-b)(s-c))
- a, b, c
- The three sides of the triangular cross-section
- s
- The semi-perimeter, half the sum of the three sides
- length
- How long the prism runs
- volume
- Triangle area times length
How to check the result by hand
- 1
Check the three sides can form a triangle
No side may be longer than the other two combined. Sides of 3, 4 and 5 pass, because 5 is less than 3 plus 4.
- 2
Compute the semi-perimeter
Add the three sides and halve. For 3, 4 and 5 the semi-perimeter is 6.
- 3
Apply Heron's formula
Multiply 6 by 3, 2 and 1 to get 36, then take the square root. The triangular face has an area of 6.
- 4
Multiply by the length for the volume
A triangle of 6 times a length of 10 gives a volume of 60. That is the primary answer for a volume question.
- 5
Add the ends for the surface area
The lateral area is the perimeter times the length, which is 120. Adding the two triangular ends of 6 each gives a total of 132.
For worked examples, common mistakes and the limits of this formula, read the full How To Calculate The Volume Of A Triangular Prism page.