Triangular Prism Calculator

Base Triangle & Length

Base triangle from

Unit

Base

Height

Prism length

The base triangle is the cross-section; the prism length is how far that triangle is extruded. Every slice perpendicular to the length is an identical copy of the base triangle.

Volume

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Enter the base triangle and prism length above to see the volume.

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Surface area

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Base area

Enter the base triangle and prism length above to see the volume, surface area, and base area.

4 min read 3 steps 6 terms 3 examples 6 FAQs baseArea = ½ × base × height

A triangular prism shows up anywhere a shape is extruded from a triangular cross-section — roof trusses, tent shapes, wedge-cut materials, and countless textbook problems.

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Walk-through

How to Use This Calculator

3 steps

Describe the base triangle

Choose how you want to define the base triangle: Base & Height (enter the triangle's base and its perpendicular height) or Three Sides (enter all three side lengths, and the calculator applies Heron's formula). Pick a display unit — inches, feet, centimeters, or meters.

Enter the prism length

Type the prism length — the distance the triangular cross-section is extruded to form the solid. This is a separate, third dimension from the base triangle's own two dimensions.

Read the volume and surface area

The Volume tab shows the volume in cubic units the instant you finish typing. Switch to the Surface Area tab for the two-triangle-plus-three-rectangle breakdown, or the Base Triangle tab to see the base area and perimeter on their own. All three tabs update together whenever you change an input.

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Reference

Formula & Methodology

4 formulas

Base area (Base & Height)

baseArea = ½ × base × height

When you know the base triangle's base and its perpendicular height, the standard triangle-area formula gives the cross-sectional area directly.

Base area (Three Sides)

baseArea = √(s(s−a)(s−b)(s−c)), s = (a+b+c)/2

Heron's formula computes the triangle's area from its three side lengths alone, with no angle or height needed. s is the semi-perimeter. The calculator first checks the triangle inequality (each side must be shorter than the sum of the other two) before applying the formula.

Volume

V = baseArea × length

A prism's volume is always its (constant) cross-sectional area times its length. For a triangular prism, that cross-section is the base triangle, so volume is simply base area multiplied by how far it's extruded.

Surface area

SA = 2 × baseArea + perimeter × length

Total surface area is the two triangular end caps (2 × baseArea) plus the three rectangular side faces, whose combined area is the base triangle's perimeter times the prism length (each rectangle is one side length wide by length long).

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Glossary

Key Terms Explained

6 terms

Triangular prism A three-dimensional solid with two parallel, congruent triangular ends (the bases) connected by three rectangular side faces. Every cross-section perpendicular to its length is an identical copy of the base triangle.

Base triangle The triangular cross-section of the prism — the shape that stays constant as you move along the prism's length. This calculator lets you define it either by base & height or by three side lengths.

Prism length The distance the base triangle is extruded to form the solid — sometimes called the prism's height or depth, but kept distinct here from the base triangle's own height to avoid confusion.

Cross-section A 2D slice of the prism taken perpendicular to its length. For a triangular prism, every cross-section is congruent to the base triangle, which is exactly why volume = base area × length.

Surface area The total area of every face of the solid: the two triangular ends plus the three rectangular sides. Computed as 2 × base area + perimeter × length.

Volume The amount of 3D space the prism occupies, measured in cubic units. Equal to the base triangle's area multiplied by the prism length.

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Scenarios

Real-World Examples

3 worked examples

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Classroom geometry problem

Base 6, height 4, length 10

Base 6 in Height 4 in Prism length 10 in

Base area = ½ × 6 × 4 = 12 in². Volume = 12 × 10 = 120 in³. Using the base's two equal slant sides (√(3²+4²) = 5), the base perimeter is 6 + 5 + 5 = 16 in, so surface area = 2 × 12 + 16 × 10 = 24 + 160 = 184 in².

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Three known side lengths

Sides 3, 4, 5 (right triangle), length 10

Side a 3 Side b 4 Side c 5 Prism length 10

Semi-perimeter s = (3+4+5)/2 = 6. Heron's formula gives base area = √(6×3×2×1) = √36 = 6. Volume = 6 × 10 = 60. Perimeter = 3+4+5 = 12, so surface area = 2 × 6 + 12 × 10 = 12 + 120 = 132.

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Triangular roof truss or beam stock

Base 8, height 6, length 20

Base 8 ft Height 6 ft Prism length 20 ft

Base area = ½ × 8 × 6 = 24 ft². Volume = 24 × 20 = 480 ft³ — the material volume of a triangular beam or roof-truss segment 20 ft long. Doubling the prism length would double the volume directly, since volume scales linearly with length once the base triangle is fixed.

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Reference

Cite This Calculator

APA & MLA

Use either format to cite this calculator in a paper, report, or resource list.

APA

MLA

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Deep Dive

Finding the volume and surface area of a triangular prism

3 chapters · 4 min read

A triangular prism shows up anywhere a shape is extruded from a triangular cross-section — roof trusses, tent shapes, wedge-cut materials, and countless textbook problems. Because the cross-section never changes along the prism's length, both its volume and surface area reduce to two simple formulas built on the base triangle's area and perimeter.

How the Triangular Prism Calculator works

The calculator first finds the base triangle's area and perimeter, then applies two prism formulas. If you supply the base and height, area is the familiar ½ × base × height. If you supply three side lengths instead, the calculator uses Heron's formula — computing the semi-perimeter s = (a+b+c)/2, then area = √(s(s−a)(s−b)(s−c)) — after first confirming the three sides actually form a valid triangle (each side must be shorter than the sum of the other two). Once the base area and perimeter are known, volume is base area × prism length, and surface area is 2 × base area (the two triangular ends) + perimeter × length (the three rectangular sides).

Inputs and what they mean

Base & Height mode assumes an isosceles base triangle for the perimeter calculation, since only the base and perpendicular height are known — the two remaining sides are treated as equal slant sides computed from the base and height via the Pythagorean theorem. This only affects the surface-area perimeter term; volume (base area × length) is exact either way. Three Sides mode is exact for both volume and surface area, since all three side lengths are known directly. The prism length is a separate input from the base triangle's own base and height — don't confuse the two when reading a diagram.

Limits and edge cases

This calculator assumes a right prism — the two triangular ends are directly opposite each other, connected by rectangular (not parallelogram) side faces. An oblique prism, where the ends are offset at an angle, has the same volume formula (base area × length, measured perpendicular to the base) but a different surface-area calculation since the side faces become parallelograms rather than rectangles. In Three Sides mode, if the entered lengths fail the triangle inequality (one side longer than the sum of the other two), the calculator flags the input as invalid rather than returning a nonsensical negative-under-the-square-root result.

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Questions

Frequently Asked Questions

6 questions

What is the formula for the volume of a triangular prism?+

V = base area × length, where the base area is the area of the triangular cross-section and length is the distance that triangle is extruded. For a base area of 12 and a length of 10, the volume is 120.

How do you find the area of the base triangle?+

Use ½ × base × height if you know the triangle's base and perpendicular height, or Heron's formula √(s(s−a)(s−b)(s−c)) — with s = (a+b+c)/2 — if you know all three side lengths instead.

What is the surface area formula for a triangular prism?+

SA = 2 × base area + perimeter × length — the two triangular ends plus the three rectangular side faces, each rectangle sized by one triangle side times the prism length.

Can I use three side lengths instead of base and height?+

Yes — switch to Three Sides mode and enter all three side lengths of the base triangle. The calculator applies Heron's formula and checks the triangle inequality before computing volume and surface area.

What units does the result use?+

Volume is reported in cubic units (in³, ft³, cm³, or m³) and surface area in squared units (in², ft², cm², or m²), matching whichever linear unit you selected for the inputs.

What is the cross-section of a triangular prism?+

The cross-section is the triangle itself — every slice perpendicular to the prism's length is an identical copy of the base triangle, which is exactly why volume = base area × length.

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