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Faces, Edges and Vertices

FoundationChallengeAQAEdexcelOCR

Faces, Edges and Vertices is a key geometry topic at GCSE Maths. This Foundation worksheet gives you exam-style questions on counting faces, edges and vertices, with a full mark scheme so you can check every method mark. Suitable for AQA, Edexcel and OCR. Download the free PDF and answers below. A cube has 6 faces, 12 edges and 8 vertices.

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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.

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Topic overview

Three-dimensional shapes are described by their faces, edges and vertices. A face is a flat surface, an edge is where two faces meet, and a vertex is a corner where edges meet.

A cube has \(6\) faces, \(12\) edges and \(8\) vertices. A square-based pyramid has \(5\) faces, \(8\) edges and \(5\) vertices, and a triangular prism has \(5\) faces, \(9\) edges and \(6\) vertices.

Counting from a drawing is unreliable because some features are hidden behind the shape. The safer method is to work systematically: count the faces you can see, then reason about how many must be hidden.

Revision notes

The three terms

A face is a flat surface, an edge is a line where two faces meet, and a vertex is a point where edges meet. The plural of vertex is vertices.

Curved shapes complicate this: a cylinder has two flat circular faces and one curved surface, and no vertices at all.

Counting systematically

Count the faces first, since they are easiest to identify, then the edges, then the vertices.

For a prism, count the two identical ends plus the rectangular sides. A triangular prism has \(2 + 3 = 5\) faces.

Hidden features

A drawing shows only some faces, edges and vertices. Dashed lines usually indicate hidden edges.

For a cube drawn on paper you can typically see three faces, but there are six in total. Reasoning about symmetry is more reliable than counting what is visible.

Key points

  • A face is a flat surface.
  • An edge is where two faces meet.
  • A vertex is a corner point.
  • A cube has 6 faces, 12 edges and 8 vertices.
  • A cylinder has no vertices.
  • Dashed lines show hidden edges.

Worked examples

Example 1

How many faces, edges and vertices does a cube have?

Working

\[6 \text{ faces}\]count the flat surfaces
\[12 \text{ edges}\]count where the faces meet
\[8 \text{ vertices}\]count the corners

Example 2

How many faces does a triangular prism have?

Working

\[2 \text{ triangular ends}\]count the identical ends
\[3 \text{ rectangular sides}\]count the connecting faces
\[5 \text{ faces}\]add them together

Example 3

How many vertices does a cylinder have?

Working

\[\text{A cylinder has curved surfaces}\]there are no corner points
\[0 \text{ vertices}\]state the answer

Common mistakes

  • Counting only the visible faces.

    A drawing hides some faces, so reason about the whole shape rather than counting what you can see.

  • Confusing edges with faces.

    An edge is a line; a face is a surface.

  • Giving a cylinder vertices.

    It has no corner points, so the answer is zero.

  • Saying vertexes.

    The plural of vertex is vertices.

Exam tips

  • Count faces first, then edges, then vertices.
  • Use symmetry to work out hidden features.
  • Look for dashed lines marking hidden edges.
  • Learn the counts for the common solids.

Key terms

Face
A flat surface of a 3D shape.
Edge
A line where two faces meet.
Vertex
A corner where edges meet.
Prism
A solid with two identical ends joined by rectangles.

Related topics

Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.