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Triangular Prism Geometry & Calculation Methods

A triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides.

Method 1: Base and Perpendicular Triangle Height

When you know the base width b and altitude h of the triangle face, plus prism length L:

• Base Area A_t = 0.5 × b × h
• Volume V = A_t × L = 0.5 × b × h × L

Method 2: Three Triangle Sides (Heron’s Formula)

When you know the three side lengths a, b, and c of the triangular end:

1. Semi-perimeter s: s = (a + b + c) / 2
2. Cross-sectional area A_t: A_t = √(s × (s - a) × (s - b) × (s - c))
3. Total volume V: V = A_t × L

Method 3: Right-Angled Triangular Prism

When two perpendicular legs a and b meet at 90 degrees:

• A_t = 0.5 × a × b
• V = 0.5 × a × b × L

Gable roof attic – calculation example

Let’s find the air volume inside a residential attic space with base width 24 ft, ridge height 8 ft, and house length 40 ft:

1. Triangle base width: base = 24 ft.
2. Triangle ridge height: height = 8 ft.
3. House length: length = 40 ft.
4. Triangle gable end area: base area = 96 sq ft.
5. The calculation results are available for you: attic volume = 3,840 cu ft (142.2 cubic yards / 108.7 m³).

💡 To calculate total surface area, add the areas of the two triangular ends to the sum of the three rectangular side faces: A_total = 2 × A_t + (a + b + c) × L.