Pentagonal Pyramid (3D) — free printable diagram

How many faces, edges and vertices a pentagonal pyramid has

A pentagonal pyramid is a 3D solid with 6 faces, 10 edges and 6 vertices. Every face is flat, so it is a polyhedron and Euler's formula applies to it.

Solid

Pentagonal pyramid

Faces

6

Edges

10

Vertices (corners)

6

Shape of the base

Pentagon

Triangular faces

5

Apex

1 — the single point where the triangles meet

Volume

V = ⅓ × area of the pentagonal base × perpendicular height

Surface area

SA = area of the pentagonal base + the areas of the five triangular faces

• A pyramid has one base and a single apex above it. This one has a pentagonal base and 5 triangular faces rising to the apex, so 5 + 1 = 6 faces altogether.
• Every pentagonal pyramid has 10 edges (2 × 5: 5 around the base and 5 rising to the apex) and 6 vertices — the 5 corners of the base plus the apex.
• 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 6 + 6 − 10 = 2.