Triangular Prism Calculator
Calculate volume and surface area of triangular prisms with multiple triangle input methods
Calculate Triangular Prism
Calculation Results
Formulas used:
Volume = Base Area × Length = 0.00 × 0 = 0.00 cm³
Surface Area = 2 × Base Area + Perimeter × Length = 2 × 0.00 + 0.00 × 0 = 0.00 cm²
Example Calculation
Tent-Shaped Prism Example
Given: Triangular tent with sides a = 60 in, b = 50 in, c = 50 in
Prism length: 80 in
Method: Three sides (SSS)
Step-by-Step Solution
1. Calculate semi-perimeter: s = (60 + 50 + 50) ÷ 2 = 80 in
2. Apply Heron's formula: Area = √[s(s-a)(s-b)(s-c)]
3. Area = √[80 × 20 × 30 × 30] = √1,440,000 = 1,200 in²
4. Volume = Area × Length = 1,200 × 80 = 96,000 in³
5. Perimeter = 60 + 50 + 50 = 160 in
6. Surface Area = 2 × 1,200 + 160 × 80 = 15,200 in²
Triangle Input Methods
Base & Height
Area = ½ × base × height
Simplest method for right triangles
Three Sides
Uses Heron's formula
When all three sides are known
Two Sides + Angle
Area = ½ × a × b × sin(C)
Angle between the two sides
Two Angles + Side
Uses law of sines
Side between the two angles
Quick Tips
A triangular prism has 5 faces, 9 edges, and 6 vertices
Volume = base area × height (prism length)
Surface area includes two triangular faces + three rectangular faces
Triangle inequality: sum of any two sides > third side
Common in architecture, engineering, and packaging
Understanding Triangular Prisms
What is a Triangular Prism?
A triangular prism is a three-dimensional geometric shape with two identical triangular bases connected by three rectangular faces. The cross-section remains constant along the entire length of the prism, making it a type of right prism.
Key Properties
- •Faces: 5 total (2 triangular, 3 rectangular)
- •Edges: 9 total (6 from triangles, 3 connecting)
- •Vertices: 6 total (3 on each triangular base)
- •Base: Triangle (any type - scalene, isosceles, equilateral)
Volume Formula
V = Base Area × Length
The volume is calculated by multiplying the area of the triangular base by the length (or height) of the prism. This formula works because the cross-section is uniform.
Surface Area Formula
SA = 2 × Base Area + Perimeter × Length
Surface area includes the areas of both triangular bases plus the areas of the three rectangular side faces.
Triangle Area Calculation Methods
Base and Height
Area = ½ × base × height
Most straightforward method when height is perpendicular to base.
Three Sides (Heron's Formula)
Area = √[s(s-a)(s-b)(s-c)]
Where s = (a+b+c)/2 is the semi-perimeter.
SAS (Two Sides and Included Angle)
Area = ½ × a × b × sin(C)
Where C is the angle between sides a and b.
ASA (Two Angles and Side Between)
Area = a² × sin(B) × sin(C) / (2 × sin(B+C))
Where a is the side between angles B and C.
Real-World Applications
🏠 Architecture
Roof trusses, triangular windows, structural supports, and decorative elements
📦 Packaging
Triangular tubes, gift boxes, specialty containers, and shipping packages
🏗️ Engineering
Bridge supports, tower structures, mechanical components, and frameworks