Surface Area of a Triangular Prism Formula

Geometry Formulas: Area, Volume, Perimeter
Formula:

What is the formula for the surface area of a triangular prism?

Answer

Surface area of a triangular prism
S = a · h + 3 · a · l

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

S = a · h + 3 · a · l

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

Related Calculations

See Also

Geometry Formulas: Area, Volume, Perimeter

These are the formulas for the area, perimeter, circumference, volume and surface area of the standard shapes — 31 of them. Each page shows not only the formula but where it comes from, what every letter stands for, two worked examples and the mistake that this particular shape invites. For example, it can help you find out what is the formula for the surface area of a triangular prism? (The answer is: S = a · h + 3 · a · l). Pick the pair — "Area of a circle", for instance — and hit the "Find out" button.
Geometry Formulas: Area, Volume, Perimeter
Formula:

Values from the Formula (a = 6, h = 5.2)

If l =Surface area
149.2 square units
267.2 square units
5121.2 square units
10211.2 square units
15301.2 square units
20391.2 square units

FAQ

What is the formula for the surface area of a triangular prism?

Surface area of a triangular prism S = a · h + 3 · a · l

Where does this formula come 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.

What is the most common mistake here?

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.

How do I use this formula?

Put your own numbers in place of the letters. With a = 4, h = 3.46, l = 7, for instance, the formula S = a · h + 3 · a · l gives = 97.84 square units.

See Also