Surface Area of Triangular Prism Calculator
Calculate the total and lateral surface area of triangular prisms with step-by-step solutions
Calculate Surface Area
Height of the triangular prism
Surface Area Results
Formula: Total Area = Lateral Area + 2 × Base Area
Perimeter: 0.00 cm
Example Calculation
Right Triangle Prism Example
Given: Right triangle with legs a = 3 cm, b = 4 cm
Prism length: L = 10 cm
Calculate hypotenuse: c = √(3² + 4²) = 5 cm
Base area: (3 × 4) / 2 = 6 cm²
Perimeter: 3 + 4 + 5 = 12 cm
Solution
Lateral area = Length × Perimeter = 10 × 12 = 120 cm²
Total surface area = 120 + 2 × 6 = 132 cm²
Triangle Types
Right Triangle
Two sides forming 90°
Use Pythagorean theorem
Three Sides
All sides known
Use Heron's formula
Angle Methods
Use trigonometry
Law of sines/cosines
Key Formulas
Total Surface Area
A = L × P + 2 × B
Lateral Surface Area
A = L × P
Right Triangle Area
A = (a × b) / 2
Heron's Formula
A = √[s(s-a)(s-b)(s-c)]
L = Length, P = Perimeter, B = Base area
Understanding Triangular Prism Surface Area
What is a Triangular Prism?
A triangular prism is a 3D shape with two parallel triangular faces (bases) and three rectangular faces (lateral surfaces) connecting corresponding sides of the triangular bases.
Surface Area Components
- •Two triangular bases: The top and bottom faces
- •Three rectangular faces: The lateral (side) surfaces
- •Total surface area: Sum of all face areas
Calculation Methods
Right Triangle
Use Pythagorean theorem for missing side
All Three Sides
Apply Heron's formula for area
With Angles
Use trigonometry and law of sines/cosines
Pro Tip: Always verify triangle inequality: sum of any two sides must be greater than the third side.