Hubs:
Top Tools:
Math β€’ Triangular Prism Volume Calculator

Triangular Prism Volume Calculator

Calculate the volume and total surface area of a triangular prism from its three cross-section sides and prism length.

Volume (V = Base Area Γ— L)
146.969
Total Surface Area
209.394
Triangular Base Area (Heron's Formula)
14.697
Be the first person to rate this calculator
AdvertisementIn-Article
Calculation Guide & Reference

Triangular Prism Volume & Surface Area Mathematics

Triangular prism calculator computes the volume and total surface area from the three sides of its triangular cross-section and prism length.

Standardized Mathematical Formula
V = Base Area Γ— L | Surface Area = 2 Γ— Base Area + Perimeter Γ— L

A triangular prism's volume is its triangular cross-section area multiplied by the prism's length, the same "base Γ— height" logic as any prism. The triangular base area is found from its three sides using Heron's formula. Total surface area adds the two triangular end caps to the three rectangular side faces.

Variables:
a, b, c:The three side lengths of the triangular cross-section
L:Length (depth) of the prism
How It Works (Step-by-Step)
  • 1Enter the three side lengths (a, b, c) of the triangular cross-section.
  • 2Enter the prism's length (L).
  • 3View the base area (via Heron's formula), volume, and total surface area.
Real-World Numerical Example
Triangle Sides 5, 6, 7 β€” Prism Length 10

A triangular prism has a cross-section with sides 5, 6, and 7 units, and a length of 10 units.

β€’Semi-perimeter: s = (5+6+7)/2 = 9.
β€’Base area (Heron's formula): √(9Γ—4Γ—3Γ—2) = √216 β‰ˆ 14.70 square units.
β€’Volume: 14.70 Γ— 10 β‰ˆ 146.97 cubic units.
β€’Surface area: (2 Γ— 14.70) + (18 Γ— 10) β‰ˆ 209.39 square units.
Result: The prism has a volume of approximately 146.97 cubic units and a surface area of about 209.39 square units.
Calculation Best Practices & Tips
Examine the discriminant (bΒ² - 4ac) before solving quadratics to instantly know if roots are real, distinct, repeated, or complex.
In statistical analysis, always check both the mean and median to identify if data distribution is skewed by outliers.
When calculating percentage changes, ensure you divide by the original starting baseline value: ((New - Old) / Old) * 100.

Frequently Asked Questions (FAQ)

A valid triangle requires each side to be shorter than the sum of the other two (the triangle inequality) β€” if that fails, no such triangle (and therefore no such prism) exists.

Yes β€” a right triangle is just a special case where the three sides satisfy the Pythagorean theorem; Heron's formula still correctly computes its area from the three side lengths alone.

Explore90 MathCalculators

Algebraic solvers, geometric area & volume, matrix operations, prime factorization, and percentages.

More in Math

Top Similar Tools (Math)

Tags:
Looking for More Calculators?

Explore more tools in Math (83+ more calculators available)

Browse our complete directory with category filters, formulas, and verified engines.