Triangular prism calculator
A triangular prism with a triangle 6 cm across and 4 cm high, 10 cm long, has a volume of 120 cm³ and a surface area of 184 cm² in the triangular prism calculator.
Volume
- Volume Volume units are the measurement unit cubed: in centimeters the answer is in cubic centimeters.
- 120 cm³
- Formula A prism: the triangle's area, half base times height, times the length. Half the box with the same base, height and length.
- V = (1/2) × b × h × L = (1/2) × 6 × 4 × 10 = 120
- Measurements used
- triangle base b = 6 cm, triangle height h = 4 cm, length L = 10 cm
- Total surface area A = bh + (b + 2s)L, s = √((b/2)² + h²).
- 184 cm²
- Lateral area (three rectangles) The triangle's perimeter times the length. The surface area assumes an isosceles triangle, whose two sloping sides are 5 cm each; the volume holds for any triangle with this base and height.
- 160 cm²
- In liters 1 liter is 1,000 cubic centimeters, the volume of a 10 cm cube.
- 0.12 L
- In US gallons A US gallon is defined as exactly 231 cubic inches, 3.785411784 liters. An imperial gallon is about 20% larger.
- 0.03170065 gal
- In other cubic units Cubic conversions cube the length factor: a yard is 3 feet, so a cubic yard is 27 cubic feet.
- 0.00012 m³ = 0.00423776 ft³ = 0.0001569541 yd³
| Every length times | Volume | Surface area |
|---|---|---|
| 0.5 | 15 cm³ (×0.125) | 46 cm² (×0.25) |
| 1 | 120 cm³ (×1) | 184 cm² (×1) |
| 2 | 960 cm³ (×8) | 736 cm² (×4) |
| 3 | 3,240 cm³ (×27) | 1,656 cm² (×9) |
| 10 | 120,000 cm³ (×1,000) | 18,400 cm² (×100) |
- Volume scales with the cube of length and surface area with the square. Double every measurement and the volume goes up 8 times while the surface only goes up 4. That is why large animals keep heat better and why small ice cubes melt faster.
How the Volume Calculator works
The triangular prism volume formula is V = ½ × b × h × L: the area of the triangle at one end, half its base times its height, times the length of the prism. For b = 6, h = 4 and L = 10, the triangle is ½ × 6 × 4 = 12 cm², and 12 × 10 = 120 cm³.
The formula for surface area of a triangular prism is A = b × h + (s₁ + s₂ + s₃) × L. The two triangular ends together make b × h, and the three rectangles are each one side of the triangle times the length.
For an isosceles triangle with a base of 6 and a height of 4, the two sloping sides are √(3² + 4²) = 5 each, so the triangle's perimeter is 16 and the surface area is 24 + 16 × 10 = 184 cm². The three rectangles alone, the lateral area, are 160 cm².
The surface area assumes an isosceles triangle, with its peak over the middle of the base. The volume holds for any triangle with that base and height. For a triangle with three different sides, add the three sides and multiply by the length for the rectangles.
A triangular prism is half the box with the same base, height and length: a 6 × 4 × 10 box holds 240 cm³.
Volume Calculator FAQ
How do I find the volume when the ends are right triangles?
Use the two legs as the base and height. Legs of 3 and 4 with a length of 10 give ½ × 3 × 4 × 10 = 60.
What is the difference between a triangular prism and a triangular pyramid?
A prism has the same triangle at both ends, joined by three rectangles. A pyramid has one triangular base and tapers to a point, and holds a third of the prism with the same base and height.
How do I find the length from the volume?
Divide the volume by the area of the triangle: 120 cm³ ÷ 12 cm² = 10 cm.
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