Pentagonal Prism (3D) — free printable diagram

How many faces, edges and vertices a pentagonal prism has

A pentagonal prism is a 3D solid with 7 faces, 15 edges and 10 vertices. Every face is flat, so it is a polyhedron and Euler's formula applies to it.

Solid

Pentagonal prism

Faces

7

Edges

15

Vertices (corners)

10

Shape of each end

Pentagon

Joining faces

5 rectangles

Volume

V = area of the pentagonal end × length

Surface area

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

• A prism has the same cross-section all the way along. This one has a pentagon at each end joined by 5 rectangles, so 5 + 2 = 7 faces altogether.
• Every pentagonal prism has 15 edges (3 × 5) and 10 vertices (2 × 5), whatever size it is drawn at and whichever way up it is standing.
• 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 7 + 10 − 15 = 2.