Case 1
- Triangle side a
- 3
- Triangle side b
- 4
- Triangle side c
- 5
- Prism length
- 10
132.000000
Open with these valuesTriangular Prism Surface Area Calculator
132.000000units²
Result: 132.000000 units²Two triangular ends plus three rectangles: total = 2 × triangle area + (a + b + c) × L. Heron's formula gets the triangle from the three sides alone, no height needed. A 3-4-5 triangle drawn out 10 long comes to 2 × 6 + 12 × 10 = 132 square units.
The numbers at a glance
Held fixed: Triangle side a 3.000, Triangle side b 4.000, Triangle side c 5.000.
| Prism length | Result |
|---|---|
| 2.500 | 42.000000 |
| 5.000 | 72.000000 |
| 7.500 | 102.000000 |
| 10.000Your value | 132.000000 |
| 12.500 | 162.000000 |
| 15.000 | 192.000000 |
| 17.500 | 222.000000 |
| 20.000 | 252.000000 |
Worked examples
Case 2
- Triangle side a
- 6
- Triangle side b
- 8
- Triangle side c
- 10
- Prism length
- 12
336.000000
Open with these valuesCase 3
- Triangle side a
- 13
- Triangle side b
- 14
- Triangle side c
- 15
- Prism length
- 20
1,008.000000
Open with these valuesHow it's calculated
S = 2√(s(s−a)(s−b)(s−c)) + (a + b + c) × L, s = ½(a + b + c)
- StepMeasure the three sides of the triangular end, in one unit.
- StepCheck each side is shorter than the other two added together.
- StepMeasure the length of the prism in that same unit.
- ResultRead the whole outside area in square units.
Reference table
| a, b, c, length | Ends + sides | Total surface |
|---|---|---|
| 1, 1, 5, 10 | no triangle: 1 + 1 is under 5 | 70 |
| 3, 4, 5, 10 | 2 × 6 + 12 × 10 | 132 |
| 5, 5, 6, 7 | 2 × 12 + 16 × 7 | 136 |
| 7, 8, 9, 4 | 24√5 + 96 | 149.665631 |
| 6, 8, 10, 12 | 2 × 24 + 24 × 12 | 336 |
| 13, 14, 15, 20 | 2 × 84 + 42 × 20 | 1008 |
Questions
How do I calculate the surface area of a triangular prism?
Add the two triangular ends to the three rectangular sides: total = 2 × triangle area + (a + b + c) × L. Take the triangle area from Heron's formula. For a 3-4-5 triangle and a length of 10 that is 2 × 6 + 12 × 10 = 132 square units.
What is the lateral surface area?
The lateral surface is the three rectangles only, without the two triangular ends, and it equals the triangle's perimeter times the length: (a + b + c) × L. For sides 3, 4, 5 and a length of 10 it is 12 × 10 = 120 square units.
What is Heron's formula and why is it used here?
Heron's formula gives a triangle's area from its three sides alone, with no height. With the semi-perimeter s = (a + b + c)/2 the area is √(s(s−a)(s−b)(s−c)); for 3-4-5 that is √(6 × 3 × 2 × 1) = 6. It lets the calculator work straight from lengths you can measure.
What if the three sides cannot form a triangle?
Three lengths only close into a triangle if each is shorter than the other two added together — sides 1, 1 and 5 fail that. This calculator then treats the end faces as empty and returns just the three rectangles, so 1, 1, 5 with length 10 gives 70 rather than an error.
Which units does the answer use?
Whatever you entered, squared. All four measurements must share one unit; centimetres give square centimetres, inches give square inches.
Sources and last check
Information, not professional advice.