The Triangular Prism Calculator multiplies the area of the triangular cross section by the prism length along the axis perpendicular to that triangle. Enter three side lengths of the triangle and the prism length, or base and height of the triangle with length. The page redraws a labelled figure showing the triangle extruded along the length.
The reference fixture uses a 3-4-5 right triangle base and length 10, giving base area 6 and volume 60. Related pages cover the Rectangular Prism Calculator for rectangular ends, the Triangle Calculator when only the planar triangle is needed, and the Surface Area Calculator for multi-shape surface queries.
Calculate the volume of a triangular prism
Volume equals base triangle area times prism length when the extrusion axis is perpendicular to the triangular faces. The Triangular Prism Calculator accepts any valid triangle area method for the base, including half base times height for a right triangle and Heron's formula when three sides are known.
V = A_triangle * LFor a right triangle with legs b and h_tri:
A_triangle = (1/2) * b * h_tri
V = (1/2) * b * h_tri * LVolume scales linearly with prism length and with the triangle area. Doubling length doubles volume. An oblique prism with the same cross-sectional area and the same perpendicular distance between end faces has the same volume; this page diagrams the right prism case.
For a 3-4-5 right triangle base and L = 10:
A_triangle = (1/2) * 3 * 4 = 6
V = 6 * 10 = 60Heron check with sides 3, 4, 5: semi-perimeter s = 6, area = sqrt(6*(6-5)*(6-4)*(6-3)) = sqrt(6*1*2*3) = sqrt(36) = 6. Same base area, same volume.
Calculate the surface area
Surface area sums two triangular ends and three rectangular side faces. Each rectangle has one side equal to a triangle edge and the other equal to prism length L. The Triangular Prism Calculator expands that sum when all three triangle sides and L are known.
SA = 2 * A_triangle + (side1 + side2 + side3) * LThe perimeter of the triangle times L is the lateral area. Adding both triangular ends completes the closed solid. Open troughs that omit one rectangular face subtract that face from the total.
For sides 3, 4, 5 and L = 10:
Lateral SA = (3 + 4 + 5) * 10 = 120
Ends = 2 * 6 = 12
Total SA = 132A rectangular prism with edges 3, 4 and 5 has volume 60 as well, but its surface area is 94, not 132. Same volume number does not imply the same solid. Keep the triangular and rectangular pages distinct.
Solve a triangular prism
Use sides 3, 4 and 5 for the base triangle and length 10 along the prism. Base area is the right-triangle half product. Volume and surface area follow. 1. Base area
A = (1/2) * 3 * 4 = 62. Volume
V = 6 * 10 = 603. Lateral surface area
Lateral SA = 12 * 10 = 1204. Total surface area
SA = 120 + 12 = 132If the triangle is not right-angled, compute area with Heron or (1/2)*ab*sin(C) before multiplying by L. The volume formula does not change; only the area step does. For angle work on the triangle alone, use the Triangle Calculator, then return here with the area.
Prism length L is measured perpendicular to the triangular faces on this page. If a drawing shows an oblique extrusion, use the perpendicular distance between the end planes as L rather than the slanted edge length along a generator. That distinction mirrors height versus slant on cones and pyramids: volume tracks the perpendicular measure.
Unit checks matter on shop drawings. A triangle with sides in centimeters and a length typed in meters will silently mis-scale volume by a factor of 100. Keep every length field on one unit system before multiplying. The result panel states cube units for volume and square units for surface area so the power of the unit is visible next to the number.
Frequently asked questions
What is triangular prism volume?
Volume is base triangle area times length. For base area 6 and length 10, V = 60.
How is base area found?
Use (1/2) * base * height for a right triangle, or Heron's formula from three sides, or (1/2)*ab*sin(C) when an included angle is known.
What is the 3-4-5 base area?
For legs 3 and 4, area is (1/2)*3*4 = 6. The hypotenuse 5 is not needed for that area step.
Must the base be a right triangle?
No. Any triangle base works with V = A * L. The 3-4-5 case is only the reference fixture.
What is total surface area?
Total surface area is 2 * A plus the triangle perimeter times L. For the reference prism, SA = 132.
How does this differ from a rectangular prism?
A rectangular prism has rectangular ends and volume l*w*h. A triangular prism has triangular ends and volume A*L.
Can the Triangular Prism Calculator use base and height of the triangle?
Yes. Enter triangle base and height to form A = (1/2)*base*height, then multiply by prism length.
What units does the Triangular Prism Calculator use?
Triangle sides and prism length share one length unit. Volume uses cube units; surface area uses square units.
How do I use Heron's formula for the base?
With sides a, b, c, set s = (a+b+c)/2 and A = sqrt(s*(s-a)*(s-b)*(s-c)). For 3, 4, 5, s = 6 and A = 6, matching the right-triangle half product.
What if one rectangular face is open?
Subtract that face's area (triangle side times L) from the closed total surface area 132 in the reference case, or from (perimeter)*L + 2*A in general.
Does the Triangular Prism Calculator draw the net?
The page shows a solid figure with the triangle extruded. Face areas in the surface formula match the rectangles and triangles that would appear on a net.
What is the perimeter of the 3-4-5 base?
Perimeter is 3 + 4 + 5 = 12. Lateral surface area is that perimeter times length 10, which equals 120.
Can angles be entered for the triangle?
When two sides and the included angle are known, area is (1/2)*ab*sin(C). Convert that area, then multiply by prism length for volume.
Summary
Triangular Prism Calculator returns volume and surface area from a triangular cross section and prism length, with substituted arithmetic and a labelled figure. Worked numbers match the 3-4-5 base and length 10: area 6, volume 60, lateral SA 120 and total SA 132.
Keep length perpendicular to the triangular ends when reading a drawing. Heron and right-triangle area routes both yield base area 6 on that fixture. Use the Rectangular Prism Calculator for box solids and the Triangle Calculator for planar triangle solving.