Triangular Prism Calculator
Calculate volume, surface area, and other properties of a triangular prism
Calculation Results
Enter triangular prism measurements to calculate all properties.
Base Area (B): square units
Height (h): units
Volume (V): cubic units
Lateral Area (L): square units
Surface Area (S): square units
Base Perimeter (P): units
Triangular Prism Diagram
Δ =Triangular Prism Formulas
Key Properties
- Base Area (B): Area of the triangular base
- Height (h): Distance between the two triangular bases
- Volume (V): Space contained within the prism
- Lateral Area (L): Area of the three rectangular faces
- Surface Area (S): Total area including both triangular bases
- Base Perimeter (P): Perimeter of the triangular base
Calculation Formulas
- Base Area (B): B = ½ × b × hΔ
- Volume (V): V = B × h
- Lateral Area (L): L = P × h
- Surface Area (S): S = L + 2B
- Base Perimeter (P): P = a + b + c
Where: b = base length of triangle, hΔ = height of triangle, a, c = other two sides of triangle, h = height of prism (length)
Example Calculation
For a triangular prism with:
Base (b) = 6 units, Triangle height (hΔ) = 4 units, Sides a = 5 units, c = 5 units, Prism height (h) = 10 units.Calculations:
- Base Area = ½ × 6 × 4 = 12 units²
- Base Perimeter = 5 + 6 + 5 = 16 units
- Volume = 12 × 10 = 120 units³
- Lateral Area = 16 × 10 = 160 units²
- Surface Area = 160 + (2 × 12) = 184 units²
About Triangular Prisms
A triangular prism is a three-dimensional shape with two identical triangular bases connected by three rectangular lateral faces. It has 5 faces, 9 edges, and 6 vertices.
Real-World Applications
- Optics: Triangular prisms are used to refract and disperse light
- Architecture: Roof structures often use triangular prism shapes
- Packaging: Some chocolate bars (like Toblerone) use this shape
- Engineering: Structural components in bridges and towers
Types of Triangular Prisms
- Regular: Equilateral triangle bases
- Right: Triangular bases are right triangles
- Isosceles: Isosceles triangle bases
- Scalene: Scalene triangle bases
Triangular Prism Components
Base Area (B)
B = ½ × b × hΔ
Prism Height (h)
Lateral Area (L)
L = P × h
Surface Area (S)
S = L + 2B
Base Perimeter (P)
P = a + b + c
Volume (V)
V = B × h
How to Use the Triangular Prism Calculator
The Triangular Prism Calculator helps compute various properties based on input values. Here's how to use it:
1. Select Calculation Method
Choose what measurements you know:
- Base Dimensions & Height - Enter triangle sides and prism height
- Base Area & Height - When you know the base area
- Volume & Height - To find the base area
- Lateral Area & Height - To find the base perimeter
- Base Length, Triangle Height & Prism Height - Simplified calculation
2. Enter Your Values
Input positive numbers in the appropriate fields:
Example 1: Base (b) = 6, Triangle Height = 4, Side a = 5, Side c = 5, Prism Height = 10
Example 2: Base Area = 12, Prism Height = 10
3. Get Results
The calculator will compute all properties:
- Base Area (B)
- Prism Height (h)
- Volume (V)
- Lateral Area (L)
- Surface Area (S)
- Base Perimeter (P)
Practical Applications
- Calculate material needed for triangular roof structures
- Determine paint required for triangular prism-shaped objects
- Find storage capacity of triangular containers
- Solve geometry problems involving triangular prisms
Frequently Asked Questions
A triangular prism has two triangular bases and three rectangular faces, while a triangular pyramid (tetrahedron) has one triangular base and three triangular faces meeting at a point.
No, a triangular prism always has two triangular faces and three rectangular faces. However, if the triangular bases are equilateral and the prism height equals the triangle side length, all rectangular faces will be square.
Use the formula: h = V / B where V is volume and B is base area.