🔺 Triangular Prism Calculator
Calculate volume, surface area, and other properties of a triangular prism
Triangle Base Dimensions
How to Use This Calculator
Enter Triangle Base Dimensions
Input the lengths of the three sides (a, b, c) of the triangular base. These can be any triangle (equilateral, isosceles, or scalene).
Enter Height
Input the height (h) of the prism, which is the perpendicular distance between the two triangular bases.
Get All Properties
Click "Calculate" to get volume, total surface area, lateral area (three rectangular sides), and base area (one triangular base).
Formulas
Base Area = √[s(s-a)(s-b)(s-c)] (Heron's Formula)
Where s = (a + b + c)/2 (semi-perimeter)
Volume = Base Area × Height
Base area multiplied by prism height
Lateral Area = Perimeter × Height = (a + b + c) × h
Sum of areas of three rectangular faces
Total Surface Area = Lateral Area + 2 × Base Area
Lateral area plus both triangular bases
Where:
- a, b, c = lengths of the three sides of the triangular base
- h = height of the prism (perpendicular distance between bases)
- s = semi-perimeter = (a + b + c)/2
- Base Area = area of one triangular base (using Heron's formula)
- Volume = space inside the prism
- Lateral Area = area of three rectangular side faces
Example 1: Triangular prism with base sides a=3, b=4, c=5, height=10
s = (3 + 4 + 5)/2 = 6
Base Area = √[6(6-3)(6-4)(6-5)] = √[6×3×2×1] = √36 = 6 units²
Volume = 6 × 10 = 60 units³
Lateral Area = (3+4+5) × 10 = 12 × 10 = 120 units²
Total Surface Area = 120 + 2×6 = 132 units²
Example 2: Equilateral triangular prism with side=6, height=8
Base Area = (6² × √3)/4 = 36√3/4 = 9√3 ≈ 15.59 units²
Volume = 15.59 × 8 = 124.72 units³
Lateral Area = (6+6+6) × 8 = 18 × 8 = 144 units²
Total Surface Area = 144 + 2×15.59 = 175.18 units²
About Triangular Prism Calculator
A triangular prism is a 3D shape with two parallel, identical triangular bases connected by three rectangular faces. This calculator finds volume, total surface area, lateral area, and base area using Heron's formula for the triangular base and standard prism formulas.
When to Use This Calculator
- Architecture: Calculate volumes and surface areas for triangular prism structures or roofs
- Engineering: Determine material requirements for triangular prism components
- Construction: Estimate materials (concrete, paint, tiles) for triangular prism buildings
- Mathematics Education: Teach students about 3D geometry and Heron's formula
- Design: Plan volumes and surface coverage for triangular prism objects
- Packaging: Calculate capacity and material needed for triangular prism packages
Why Use Our Calculator?
- ✅ Any Triangle: Works with equilateral, isosceles, or scalene triangles
- ✅ Complete Properties: Calculates volume, surface area, lateral area, and base area
- ✅ Instant Results: Get all measurements immediately
- ✅ Heron's Formula: Automatically calculates base area for any triangle
- ✅ Step-by-Step Display: See all calculations with formulas
- ✅ Completely Free: No registration required
Understanding Triangular Prisms
A triangular prism consists of:
- Two Triangular Bases: Parallel, identical triangles (any triangle type)
- Three Rectangular Faces: Rectangles connecting corresponding sides of the bases
- Volume: Base area × height (space inside)
- Base Area: Calculated using Heron's formula: √[s(s-a)(s-b)(s-c)]
- Lateral Area: Sum of three rectangular faces = Perimeter × Height
- Total Surface Area: Lateral area + 2 × base area
Real-World Applications
Construction: A triangular prism roof has base sides 8 m, 10 m, 12 m and height 4 m. Base area ≈ 39.69 m², Volume = 158.76 m³ (airspace). Total surface area = 199.38 m² (roofing material needed).
Engineering: A triangular prism component with sides 5 cm, 6 cm, 7 cm and height 10 cm has base area ≈ 14.70 cm², Volume = 147 cm³ (material volume), and total surface area = 209.40 cm² (finishing area).
Packaging: A triangular prism box with equilateral base (side 6 cm) and height 8 cm has base area ≈ 15.59 cm², Volume = 124.72 cm³ (capacity), and total surface area = 175.18 cm² (wrapping material).
Frequently Asked Questions
What is Heron's formula?
Heron's formula calculates the area of any triangle when you know all three sides: Area = √[s(s-a)(s-b)(s-c)], where s = (a+b+c)/2 is the semi-perimeter. This works for any triangle, not just right triangles.
Does this work for any triangle?
Yes! This calculator works for equilateral (all sides equal), isosceles (two sides equal), or scalene (all sides different) triangles. Heron's formula works for any triangle as long as the three sides can form a valid triangle.
How is volume different from surface area?
Volume measures the space inside the prism (cubic units). Surface area measures the total area covering the outside (square units). Volume = Base Area × Height, while Surface Area = Lateral Area + 2 × Base Area.
What if I know the base area instead of side lengths?
If you know the base area directly, you can calculate volume = Base Area × Height. However, you'd still need the perimeter (or side lengths) to calculate lateral area and total surface area.
Can I use this for a right triangular prism?
Yes! A right triangular prism is just a triangular prism where the edges are perpendicular to the bases. The formulas are the same. Enter the three sides of the triangle base and the height.
What's the difference between lateral and total surface area?
Lateral surface area includes only the three rectangular side faces (Perimeter × Height). Total surface area includes the lateral area plus both triangular bases (Lateral Area + 2 × Base Area).