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Triangular Prism Calculator

Calculate volume, surface area, and lateral area of a triangular prism. Enter triangle dimensions and prism length.

Calculator

Triangle Input Method:

Triangle Base (b)

Triangle Height (h_t)

Prism Length (l)

Triangular Prism Diagram

Triangular Prism Formulas

Using Base & Height:

Base Area: A = ½ × b × h_t
Volume: V = A × l = ½ × b × h_t × l
Lateral Area: LA = Perimeter × l
Surface Area: SA = 2A + LA

Using Heron's Formula:

Semi-perimeter: s = (a + b + c) / 2
Base Area: A = √[s(s-a)(s-b)(s-c)]
Perimeter: P = a + b + c

Understanding Triangular Prisms

A triangular prism is a 3D shape with two parallel triangular bases connected by three rectangular faces. The volume equals the base area times the length (height) of the prism.

Properties:

5 faces - 2 triangular bases + 3 rectangular sides
9 edges - 6 on the triangles + 3 connecting them
6 vertices - 3 on each triangular base
Cross-section parallel to bases is always the same triangle

Real-World Examples:

Toblerone chocolate, tent shapes, roofs, cheese wedges, and some architectural elements.

Frequently Asked Questions

How do I find the base area if I only know the three sides?

Use Heron's formula: First find the semi-perimeter s = (a+b+c)/2, then Area = √[s(s-a)(s-b)(s-c)].

What is the difference between lateral and total surface area?

Lateral area includes only the three rectangular sides. Total surface area adds the two triangular bases.

Can the triangular base be any type of triangle?

Yes! The formulas work for any triangle: equilateral, isosceles, scalene, right, or any valid triangle.

What if my prism is tilted (oblique)?

For volume, use the perpendicular height (distance between bases). The lateral surface becomes more complex with parallelograms instead of rectangles.

How is this different from a pyramid?

A prism has two identical parallel bases; a pyramid has one base that tapers to a point. The volume formula for a pyramid has a factor of 1/3.

What about equilateral triangular prisms?

For an equilateral triangle with side s: Base Area = (s²√3)/4. All three rectangular faces are identical.

Related Calculators

Triangle Area Prism Volume Cylinder Pyramid

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