Surface Area of a Triangular Prism Calculator

Surface Area of a Triangular Prism

A triangular prism has two congruent triangular bases and three rectangular lateral faces. The total surface area combines both triangular bases and the lateral surface.

$$A_t = 2A_{base} + A_l$$

The lateral surface area equals the base perimeter times the prism length:

$$A_l = (a + b + c) \times L$$

For the triangular base area, use Heron's formula with semi-perimeter $s = (a + b + c) / 2$:

$$A_{base} = \sqrt{s(s-a)(s-b)(s-c)}$$

Example

A prism with triangle sides 5, 6, and 7 cm and length 12 cm has base perimeter 18 cm, so the lateral area is $18 \times 12 = 216$ cm².

Frequently Asked Questions

What is the lateral surface of a triangular prism?

The lateral surface consists of the three rectangular faces that connect the two triangular bases. Its area equals the base perimeter multiplied by the prism length.

Can any three side lengths form a triangle?

No. The three sides must satisfy the triangle inequality: the sum of any two sides must be greater than the third side.

How is this different from a triangular pyramid?

A prism has two parallel triangular bases connected by rectangles. A pyramid has one triangular base and three triangular faces meeting at a point.

When should I use Heron's formula?

Use Heron's formula when you know all three side lengths of the triangular base but not the height of the triangle.

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Surface Area of a Triangular Prism Calculator