The Triangular Prism Surface Area Calculator calculates the total surface area of a prism with triangular ends by adding the two triangle areas to the three rectangular side faces.
Enter the triangle dimensions and the prism length below to calculate the surface area.
Triangular Prism Surface Area Calculator
Surface area of a triangular prism from the three triangle sides, a right triangle, or an equilateral triangle, plus the prism length.
The formula is A = 2B + (a + b + c) × L, where B is the area of one triangle and L is the prism length. You can enter the triangle as three sides, as a right triangle (two legs), or as an equilateral triangle (one side).
Formula
A = 2B + (a + b + c) × L
Where:
- A = total surface area
- B = area of one triangular end
- a, b, c = the three sides of the triangle
- L = length of the prism (distance between the two triangles)
Triangle area for each mode
- Three sides (Heron’s formula): B = √(p(p − a)(p − b)(p − c)), where p = (a + b + c) ÷ 2
- Right triangle: B = ½ × a × b, and the hypotenuse c = √(a² + b²)
- Equilateral triangle: B = (√3 ÷ 4) × a², so A = (√3 ÷ 2)a² + 3aL
How the Calculation Works
Step 1: Find the area of one triangular end (B) using the method that matches what you know.
Step 2: Find the lateral area: the perimeter of the triangle (a + b + c) multiplied by the prism length. This equals the three rectangles added together.
Step 3: Add two triangles and the lateral area: A = 2B + lateral area.
Variables Explained
| Variable | Meaning | Unit |
|---|---|---|
| a, b, c | Sides of the triangular end | cm, m, in, ft |
| L | Prism length | cm, m, in, ft |
| B | Area of one triangle | cm², m², in², ft² |
| A | Total surface area | cm², m², in², ft² |
Example Calculation
3-4-5 triangle prism
Given: sides a = 3 cm, b = 4 cm, c = 5 cm; prism length L = 10 cm
Triangle area: p = (3 + 4 + 5) ÷ 2 = 6, so B = √(6 × 3 × 2 × 1) = √36 = 6 cm²
Lateral area: (3 + 4 + 5) × 10 = 120 cm²
Calculation: A = 2 × 6 + 120
Result: A = 132 cm²
Equilateral triangle prism
Given: side a = 4 cm, L = 10 cm
Calculation: A = (√3 ÷ 2) × 16 + 3 × 4 × 10 = 13.856 + 120
Result: A ≈ 133.86 cm²
Common Area Conversion Table
| Unit | Equivalent |
|---|---|
| 1 m² | 10,000 cm² |
| 1 ft² | 144 in² |
| 1 m² | 10.7639 ft² |
| 1 in² | 6.4516 cm² |
Shape Properties
A triangular prism has 5 faces (2 triangles and 3 rectangles), 9 edges and 6 vertices. Each rectangle has the prism length as one side and one triangle side as the other, which is why the lateral area equals perimeter × length.
Triangle side check
Three sides can only form a triangle if any two of them add up to more than the third. The calculator warns you if the sides you enter cannot make a triangle.
Dimensions Explained
Prism length vs triangle height
The prism length is the distance between the two triangular ends. The triangle’s height is measured inside the triangle. They are different measurements; this calculator does not need the triangle height because it works from the sides.
Using base and height instead
If you know a triangle’s base and height, B = ½ × base × height. For a right triangle, the two legs are the base and height, so use the Right triangle mode.
Frequently Asked Questions
How do you find the surface area of a triangular prism?
Add the areas of the two triangles to the areas of the three rectangles: A = 2B + (a + b + c) × L.
What is the lateral surface area of a triangular prism?
It is the area of the three rectangular faces only: (a + b + c) × L, the triangle perimeter times the prism length.
How many faces does a triangular prism have?
Five: two triangular faces and three rectangular faces.
How do you find the surface area of a triangular prism with only the sides?
Use Heron’s formula to get the triangle area from its three sides, then apply A = 2B + (a + b + c) × L. The Three sides mode does this for you.
What is the surface area of a right triangular prism?
For legs a and b and prism length L: A = ab + (a + b + √(a² + b²)) × L. With legs 3 and 4 cm and length 10 cm, A = 132 cm².
Is a triangular prism the same as a triangular pyramid?
No. A prism has two parallel triangular ends joined by rectangles. A triangular pyramid (tetrahedron) has four triangular faces that meet at a point.