🔺 Surface Area of a Triangular Prism Calculator
Calculate the surface area 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 Surface Area
Click "Calculate Surface Area" to get the total surface area (all faces), 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)
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)
- 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
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
Lateral Area = (6+6+6) × 8 = 18 × 8 = 144 units²
Total Surface Area = 144 + 2×15.59 = 175.18 units²
About Surface Area of a Triangular Prism Calculator
A triangular prism is a 3D shape with two parallel, identical triangular bases connected by three rectangular faces. This calculator finds the total surface area using Heron's formula for the triangular base area and the formula for lateral area (perimeter × height).
When to Use This Calculator
- Architecture: Calculate surface area for triangular prism structures or roofs
- Engineering: Determine material requirements for triangular prism components
- Construction: Estimate paint, tiles, or cladding needed for triangular prism buildings
- Mathematics Education: Teach students about 3D geometry and Heron's formula
- Design: Plan surface coverage for triangular prism objects
- Packaging: Calculate wrapping material needed for triangular prism packages
Why Use Our Calculator?
- ✅ Any Triangle: Works with equilateral, isosceles, or scalene triangles
- ✅ Instant Results: Get accurate surface area calculations immediately
- ✅ Complete Breakdown: Shows base area, lateral area, and total surface area separately
- ✅ Heron's Formula: Automatically calculates base area using Heron's formula
- ✅ 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
- Base Area: Calculated using Heron's formula: √[s(s-a)(s-b)(s-c)]
- Lateral Area: Sum of three rectangular faces = (a + b + c) × h
- 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, Lateral area = 30 × 4 = 120 m², Total surface area = 120 + 2×39.69 = 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 and total surface area = 180 + 29.40 = 209.40 cm² (surface finishing area).
Packaging: A triangular prism box with equilateral base (side 6 cm) and height 8 cm has base area ≈ 15.59 cm² and total surface area = 144 + 31.18 = 175.18 cm² (wrapping material needed).
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.
What if I know the base area instead of side lengths?
If you know the base area directly, you can skip Heron's formula. Total surface area = Lateral area + 2 × Base area, where Lateral area = Perimeter × Height. You'd still need the perimeter or side lengths for lateral area.
How is lateral area calculated?
Lateral area = Perimeter of triangle × Height of prism. The perimeter is the sum of the three triangle sides (a + b + c). This gives the total area of the three rectangular side faces.
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 total and lateral surface area?
Total surface area includes all faces (two triangular bases + three rectangular sides). Lateral surface area includes only the three rectangular side faces, excluding the triangular bases. Lateral = Perimeter × Height.