Square Pyramid (3D Shape) — free printable clipart

How many faces, edges and vertices a square pyramid has

A square pyramid is a 3D solid with 5 faces, 8 edges and 5 vertices. Every face is flat, so it is a polyhedron and Euler's formula applies to it.

Solid

Square pyramid

Faces

5

Edges

8

Vertices (corners)

5

Shape of the base

Square

Triangular faces

4

Apex

1 — the single point where the triangles meet

Volume

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

Surface area

SA = area of the square base + the areas of the four triangular faces

• A pyramid has one base and a single apex above it. This one has a square base and 4 triangular faces rising to the apex, so 4 + 1 = 5 faces altogether.
• Every square pyramid has 8 edges (2 × 4: 4 around the base and 4 rising to the apex) and 5 vertices — the 4 corners of the base plus the apex.
• This is the shape of the Egyptian pyramids, and the one students usually picture when they hear “pyramid”.
• The perpendicular height runs from the apex straight down to the centre of the base; the slant height runs from the apex down the middle of a triangular face. The volume formula needs the first, the surface area needs the second, and swapping them is the usual source of a wrong answer.
• 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 + 5 − 8 = 2.