Triangular Prism Formulas (Volume, Surface Area)

A triangular prism has two parallel triangular bases joined by three rectangles. Its volume is V = (base area)·L, the triangle’s area times the prism length L. Its surface area is SA = 2·(base area) + (a + b + c)·L.

Triangular Prism formulas

Volume: $V = A_{base}\cdot L$
Surface area: $SA = 2A_{base} + (a+b+c)L$

where a, b, c = base triangle sides, L = prism length, A_base = area of triangular base

Volume

V = A_{base}\cdot L

Worked example

A prism with a 3-4-5 triangular base (area 6) and length 7 has volume 42 cubic units.

V = A_{base}\cdot L = 6\cdot 7 = 42

Surface area

SA = 2A_{base} + (a+b+c)L

Interactive triangular prism explorer

Drag a slider (or type a value, or use the arrow keys) and watch the diagram, the results, and the full step-by-step substitution update live.

Side a a

Base / side b b

Side c c

Prism length L

Volume V 42units³

Surface area SA 96units²

Base area A_b 6units²

Step-by-step substitution

base area = √(s(s−a)(s−b)(s−c)) = 6
V = base area · L = 6 · 7 = 42
SA = 2·base + (a+b+c)·L = 12 + 84 = 96

Classroom use: triangular prism formulas

Who it's for: Grades 7–10 · Students extending prism volume beyond rectangular bases, usually right after rectangular prisms.

Learning objectives

After using this page, students will be able to:

Compute prism volume using V = Bh with a triangular base.
Compute surface area as two triangular bases plus three rectangular faces.
Generalise V = Bh to any prism.

Suggested classroom activity

Ask students to state the volume rule for a rectangular prism, then for a triangular one, then for a prism with any base at all. The explorer confirms each case, and the generalisation to V = Bh is theirs rather than yours.

Standards alignment

Aligned to the Common Core State Standards for Mathematics. Codes are given exactly as published so they can be matched against state crosswalks.
Code	Standard
`6.G.A.4`	Represent 3-D figures using nets and use the nets to find surface area.
`7.G.B.6`	Solve real-world problems involving area, volume, and surface area of 2-D and 3-D objects.

Free to use and adapt in class under the terms on our license page — no account, no sign-up, no ads. Content last reviewed August 2026.

Related & next steps

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Frequently asked questions

How do you find the volume of a triangular prism?

Multiply the area of the triangular base by the prism’s length: V = (base area)·L. A base of area 6 and length 7 gives volume 42 cubic units.

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