Triangular Prism Volume Formula: How to Calculate It

What a prism is: bases, lateral faces, edges

A prism is a solid with two congruent polygon bases on parallel planes, joined by parallelogram-shaped lateral faces that connect matching sides of the two bases. The sides of those lateral faces are called edges. When the edges are perpendicular to the bases, the prism is right; when the bases are regular polygons, the prism is regular; when the bases are parallelograms, the solid is called a rectangular box (or parallelepiped). In the most common case, with rectangular bases, the shape is a rectangular prism, whose volume comes from multiplying length by width by height. This family of shapes belongs to solid geometry, which covers volume and surface-area rules for every three-dimensional figure, while the underlying ideas of polygon, angle, and plane come from Euclidean geometry.

The general prism volume formula

A prism’s volume comes from multiplying base area by height: V = B × h, where B is the area of the base polygon and h is the perpendicular distance between the two bases. The formula does not care what shape the base is — triangle, rectangle, or any other polygon work the same way, because volume depends only on the base’s shape and the gap between the two parallel planes that hold it. Working out B is arithmetic applied to area formulas, while rearranging V = B × h with letters standing in for numbers is basic algebra.

Triangular prism volume, step by step

For a triangular prism, the general formula applies with B swapped for the triangle’s area: find the base triangle’s area first (half its base times its height), then multiply that result by the prism’s height. It is the same two-step process used for any polygon-based prism — only the formula for B changes.

Right or oblique: which height to use

In an oblique prism, the lateral edges lean relative to the bases. Even then, the height that belongs in the formula is still the perpendicular distance between the two bases — never the lateral edge, which runs longer because it is slanted. Cavalieri’s principle explains why: when two solids’ cross-sections carry equal area at every level, the two solids share the same volume, regardless of how far their sides lean. A prism’s cross-sections stay congruent to its base even once the solid tilts, somewhat like a stack of cards fanned out sideways — the shape of each individual card never changes.

Worked example: a triangular prism has a right-triangle base with legs of 3 cm and 4 cm (so the hypotenuse measures 5 cm) and a prism height of 10 cm. The base area is half the product of the two legs: ½ × 3 × 4 = 6 cm². The volume then follows from base area times prism height: 6 cm² × 10 cm = 60 cm³.

Right triangular prism volume across base shapes

A right triangular prism is the case that shows up most often in classroom problems, but the same logic carries over to any other base polygon — only the way of finding B changes.

A second example, with an equilateral triangle of side 12 cm and a triangle height of 10.39 cm, gives a base area of about 62.34 cm² (½ × 12 × 10.39): with a 10 cm prism height, the volume works out to 623.4 cm³. The numbers change, but the process is identical to the one above: base area first, then multiply by height.