Triangular Prism (3D) — free printable diagram

How many faces, edges and vertices a triangular prism has

A triangular prism is a 3D solid with 5 faces, 9 edges and 6 vertices. Every face is flat, so it is a polyhedron and Euler's formula applies to it.

Solid

Triangular prism

Faces

5

Edges

9

Vertices (corners)

6

Shape of each end

Triangle

Joining faces

3 rectangles

Volume

V = area of the triangular end × length

Surface area

SA = 2 × (area of the triangle) + (perimeter of the triangle × length)

• A prism has the same cross-section all the way along. This one has a triangle at each end joined by 3 rectangles, so 3 + 2 = 5 faces altogether.
• Every triangular prism has 9 edges (3 × 3) and 6 vertices (2 × 3), whatever size it is drawn at and whichever way up it is standing.
• It is the prism students most often miscount, because the triangular ends look like the “top and bottom” of a shape standing on a rectangle. Whichever way it is drawn, the two triangles are the ends and the three rectangles join them.
• Euler's formula holds for every solid with flat faces: faces + vertices − edges = 2. It is the quickest way to check a count you are unsure of. Here that is 5 + 6 − 9 = 2.