Surface Area of a Triangular Prism Formula
What is the formula for the surface area of a triangular prism?
Answer
Here a is the side (or base), h is the height, perpendicular to the base, l is the slant height of a face, or the length along the solid. The result comes out in square units.
Where the formula comes from
Two triangular ends of ½·a·h each — together a·h — plus three rectangular sides. This form assumes the triangle is equilateral, so all three rectangles are a by l, giving 3·a·l. For a triangle with unequal sides, add the three rectangles one by one.
Worked examples
Let a = 6, h = 5.2, l = 10. Then the surface area of a triangular prism = 211.2 square units.
Let a = 4, h = 3.46, l = 7. Then the surface area of a triangular prism = 97.84 square units.
The common mistake
Applying the 3·a·l part to a prism whose triangle is not equilateral. Then the three rectangles are no longer all the same width — an isosceles triangle still gives two equal ones — and they have to be added side by side; only the a·h part survives unchanged.
Other quantities: Triangular prism
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See Also
- Square Footage Calculator - Width × length in feet to square feet
- Square Feet to Square Meters (Sq Ft to Sq M) - Convert Square Feet to Square Meters
- Square Meters to Square Feet (Sq M to Sq Ft) - Convert Square Meters to Square Feet
- Gravel Calculator - Area to cubic yards, tons and coverage
- Topsoil Calculator - Cubic yards, weight and coverage for any area
- Multiplication Facts - Any two numbers from 1 to 9, with the working shown
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Values from the Formula (a = 6, h = 5.2)
| If l = | Surface area |
|---|---|
| 1 | 49.2 square units |
| 2 | 67.2 square units |
| 5 | 121.2 square units |
| 10 | 211.2 square units |
| 15 | 301.2 square units |
| 20 | 391.2 square units |