Surface Area of a Triangular Prism: Complete Calculation Guide
Calculate triangular prism surface area using SA = 2B + P×L. Complete guide with worked examples and applications.
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The surface area of a triangular prism includes two triangular bases and three rectangular lateral faces. Whether you're wrapping a package, painting a structure, or estimating material costs, understanding how to calculate this surface area is essential.
The Formula
Where B is the base triangle area, P is the perimeter of the base, and L is the prism length.
Components
- Two triangular bases: 2 × B
- Three rectangular faces: P × L (sum of all three sides × length)
- Total SA: Sum of all five faces
Worked Example
Calculate the surface area of a right triangular prism with base 6 cm, height 4 cm, and length 10 cm:
- Base area: B = ½ × 6 × 4 = 12 cm²
- Hypotenuse: √(6² + 4²) ≈ 7.21 cm
- Perimeter: P = 6 + 4 + 7.21 = 17.21 cm
- Surface area: SA = 2(12) + 17.21 × 10 = 196.1 cm²
Total vs Lateral Area
Lateral area = P × L (only the three rectangular faces). Total SA = 2B + lateral area (includes both triangular bases).
Applications
- Construction: Roof and tent surface calculations
- Packaging: Material estimation for triangular boxes
- Manufacturing: Surface finishing requirements