Surface Area of Triangular Prism Calculator
Enter the three sides of the triangle and the prism length to find the total surface area.
Updated
Surface Area of Triangular Prism Calculator
Our Surface Area of Triangular Prism Calculator finds the total area of all five faces of a triangular prism from the three sides of its triangle and its length. It shows the working, the base area by Heron's formula, the two triangle ends, the three rectangle sides, the volume, the area in other units and a drawing to scale.
Quick answer
The surface area of a triangular prism is A = 2B + (a + b + c) × L, where B is the area of the triangle, a, b and c are its sides and L is the prism length. A prism with a 3, 4, 5 cm triangle and length 10 cm has A = 2 × 6 + 12 × 10 = 132 cm².
- Five faces: two equal triangles (the ends) and three rectangles (the sides)
- Triangle area: Heron's formula B = √(s(s − a)(s − b)(s − c)), s = (a + b + c) ÷ 2
- Three sides only: perimeter × length, so the same prism gives 120 cm²
- Units: the area is in square units, so sides in cm give cm²
What Is the Surface Area of a Triangular Prism?
A triangular prism is a 3D shape with two equal triangles at its ends joined by three rectangles, like a tent, a wedge or a chocolate bar box. It has 5 faces, 9 edges and 6 corners. The surface area A is the total area of its outside: how much fabric covers a tent or how much card makes the box. It is measured in square units such as cm² or m².
Triangular Prism Surface Area Formulas
Each rectangle side is one side of the triangle times the length L, so the three sides together are the triangle's perimeter times L.
| Surface | Formula |
|---|---|
| All 5 faces | A = 2B + (a + b + c)L |
| Two ends | 2B |
| Three sides | (a + b + c) × L |
| Base (B) | √(s(s − a)(s − b)(s − c)) |
| Right angle | B = ½ × leg × leg |
| Equilateral | (√3 ÷ 2)a² + 3aL |
The same prism has volume V = B × L. See the Volume of Triangular Prism Calculator.
The Net of a Triangular Prism
Unfold a triangular prism and it lies flat as a net: three rectangles in a row, each L long, with a triangle on either side. For a 3, 4, 5 cm triangle and L = 10 cm:
sides: 30 + 40 + 50 = 120 cm²
A = 12 + 120 = 132 cm²
Finding the Base Area With Heron's Formula
When you know the three sides but not the triangle's height, Heron's formula gives its area. First halve the perimeter to get s, then multiply s by its gap to each side and take the square root. For sides 6, 7 and 9 cm:
B = √(11 × 5 × 4 × 2)
B = √440 = 2√110 ≈ 20.976
L = 10: A = 2B + 22 × 10
A = 220 + 4√110 ≈ 261.952
If the three sides fail the triangle rule (the two shorter sides must add up to more than the longest), there is no triangle and no prism, so the calculator shows an error.
Triangular Prism Surface Area Examples
| Sides a, b, c; L | Surface area |
|---|---|
| 3, 4, 5; 10 cm | 132 cm² |
| 5, 5, 6; 10 cm | 184 cm² |
| 5, 6, 7; 12 cm | ≈ 245.39 cm² |
| 8, 10, 12; 15 cm | ≈ 529.37 cm² |
| 6, 6, 6; 20 cm | ≈ 391.18 cm² |
| 7, 9, 11; 25 cm | ≈ 737.84 cm² |
| 0.5, 1.2, 1.3; 4 m | 12.6 m² |
Right triangles (3, 4, 5) and some isosceles ones (5, 5, 6) give whole number base areas. Most other triangles give a square root, so the calculator also shows the exact form, such as 220 + 4√110.
Triangular Prism Surface Area in Real Life
- Tent: a 3 m long tent with a 2 m wide floor and 1.7 m sloping sides uses about 12.95 m² of fabric for the two ends and the two roof panels, plus a 6 m² groundsheet.
- Chocolate box: a 20 cm long box with an equilateral 3.5 cm end needs about 220.61 cm² of card.
- Skate ramp: 120 cm long, 40 cm high and 150 cm wide, the slope is about 126.49 cm, so covering every face takes about 4.78 m² of board.
- Glass prism: a 6, 6, 6 cm prism 20 cm long has about 391.18 cm² of polished glass.
Common Mistakes
- One triangle only: a closed prism has two ends, so add 2B, not B.
- Same size sides: the three rectangles are only equal when the triangle is equilateral.
- Mixing up heights: the triangle height h is not the prism length L.
- Volume instead: B × L is the volume in cubic units, not the surface area.
- Mixed units: convert first, so 2 m and 50 cm become 2 m and 0.5 m.
Key Terms
- Surface area
- All 5 faces together, 2B + (a + b + c)L.
- Base (B)
- The area of one triangle end.
- Length (L)
- The distance between the two triangle ends.
- Lateral area
- The three rectangle sides, (a + b + c)L.
- Net
- The prism unfolded flat: 3 rectangles, 2 triangles.
How to Use the Surface Area of Triangular Prism Calculator
- Enter the three sides. Type the sides a, b and c of the triangle end, such as 3, 4 and 5. Decimals and fractions such as 3/4 work.
- Enter the prism length. Type the length L, the distance between the two triangle ends, such as 10.
- Pick a unit. Choose mm, cm, m, km, in, ft, yd or mi if you want one. The unit pickers move together, so all lengths use the same unit.
- Read and copy the result. The surface area appears as you type, with the working, the exact form, the base area by Heron's formula, the two ends, the three sides, the volume and the area in other units. Press Copy to copy it, or Clear or Esc to start again.
Example: a door wedge has a 3, 4, 5 cm triangle and is 2 cm wide. Enter 3, 4 and 5 as the sides and 2 as the length, and pick cm. The surface area is 36 cm², and the volume is 12 cm³.
Who Can Use This Calculator?
Frequently Asked Questions (FAQs)
What is the formula for the surface area of a triangular prism?
A = 2B + (a + b + c) × L, where B is the area of the triangle end, a, b and c are its sides and L is the prism length. A 3, 4, 5 cm triangle with L = 10 cm gives A = 2 × 6 + 12 × 10 = 132 cm².
How many faces does a triangular prism have?
Five: two equal triangles at the ends and three rectangles along the length. It also has 9 edges and 6 corners.
How do you find the base area if you only know the three sides?
Use Heron's formula. Find s = (a + b + c) ÷ 2, then B = √(s(s − a)(s − b)(s − c)). For sides 6, 7 and 9, s = 11 and B = √440 ≈ 20.976.
What is the lateral surface area of a triangular prism?
It is the three rectangle sides only, without the triangle ends: (a + b + c) × L, the perimeter of the triangle times the length. A 3, 4, 5 cm prism 10 cm long has 120 cm² of lateral area.
What is the surface area of a prism with an equilateral triangle base?
With side a and length L, A = (√3 ÷ 2)a² + 3aL. Sides of 6 cm and L = 20 cm give about 31.18 + 360 = 391.18 cm².
Can I use the triangle base and height instead of three sides?
Only for the two ends: B = ½ × base × height. The three rectangle sides need all three side lengths. For a right triangle the legs are the base and height, and the third side is √(leg² + leg²).
Why does the calculator say the sides do not make a triangle?
The two shorter sides must add up to more than the longest one. Sides 2, 3 and 6 fail (2 + 3 is less than 6), so there is no triangle and no prism.
Is the Surface Area of Triangular Prism Calculator free?
Yes. It is completely free, needs no sign-up, and can be used as many times as you like.
Try our Surface Area of Triangular Prism Calculator to get the total surface area of any triangular prism from its three sides and length.