Worksheets · Geometry

Classifying solids worksheet for Geometry

Geometry adds structure to naming solids: Euler's formula F + V = E + 2 ties the counts together, and nets and cross-sections show which faces a solid has. A name still comes from the base, but you should be able to work backwards from two of the counts to the third.

Also taught in Pre-Algebra, at its own level and with its own examples.

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Pick more than one for a sheet that mixes them.

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Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Classifying Solids

Date Period

Answer each question about the solid.

  1. Name the solid

    Give the most specific name for the solid.
  2. Give the most specific name for the solid.
  3. Give the most specific name for the solid.
  4. Give the most specific name for the solid.
  5. Give the most specific name for the solid.

  1. Count faces, edges and vertices

    How many faces, edges and vertices does a heptagonal pyramid have?
  2. How many faces, edges and vertices does this solid have?
  3. Count the faces, edges and vertices of the solid.
  4. How many faces, edges and vertices does the solid have?
  5. How many faces, edges and vertices does a nonagonal prism have?

  1. Name solids and their properties

    A net has 20 equilateral triangles. What solid does it fold into?
  2. A prism has 12 vertices. How many edges does it have?
  3. A prism has 16 vertices. How many faces does it have?
  4. A prism has 14 faces. How many vertices does it have?
  5. A cone is sliced at a slant that cuts all the way around its curved side but does not touch the base. What shape is the cross-section?

  1. Use Euler's formula

    Exactly 4 edges meet at every vertex of a polyhedron with 16 faces. How many edges does it have?
  2. Exactly 4 edges meet at every vertex of a polyhedron with 10 faces. How many vertices does it have?
  3. A polyhedron has 20 triangular faces and 12 pentagonal faces, and no other faces. How many vertices does it have?
  4. A polyhedron has 8 triangular faces, and no other faces. How many vertices does it have?
  5. A polyhedron has 12 pentagonal faces and 20 hexagonal faces, and no other faces. How many vertices does it have?

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Classifying SolidsAnswer keyVersion 2

Date Period

Answer each question about the solid.

  1. Name the solid

    Give the most specific name for the solid.Pentagonal prism
  2. Give the most specific name for the solid.Hexagonal prism
  3. Give the most specific name for the solid.Hexagonal pyramid
  4. Give the most specific name for the solid.Hexagonal prism
  5. Give the most specific name for the solid.Pentagonal prism

  1. Count faces, edges and vertices

    How many faces, edges and vertices does a heptagonal pyramid have?F=8, E=14, V=8
  2. How many faces, edges and vertices does this solid have?F=9, E=16, V=9
  3. Count the faces, edges and vertices of the solid.F=9, E=21, V=14
  4. How many faces, edges and vertices does the solid have?F=10, E=24, V=16
  5. How many faces, edges and vertices does a nonagonal prism have?F=11, E=27, V=18

  1. Name solids and their properties

    A net has 20 equilateral triangles. What solid does it fold into?Icosahedron
  2. A prism has 12 vertices. How many edges does it have?18
  3. A prism has 16 vertices. How many faces does it have?10
  4. A prism has 14 faces. How many vertices does it have?24
  5. A cone is sliced at a slant that cuts all the way around its curved side but does not touch the base. What shape is the cross-section?Ellipse

  1. Use Euler's formula

    Exactly 4 edges meet at every vertex of a polyhedron with 16 faces. How many edges does it have?28
  2. Exactly 4 edges meet at every vertex of a polyhedron with 10 faces. How many vertices does it have?8
  3. A polyhedron has 20 triangular faces and 12 pentagonal faces, and no other faces. How many vertices does it have?30
  4. A polyhedron has 8 triangular faces, and no other faces. How many vertices does it have?6
  5. A polyhedron has 12 pentagonal faces and 20 hexagonal faces, and no other faces. How many vertices does it have?60

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

A polyhedron has 7 faces and 15 edges. How many vertices does it have?

  1. Euler: F + V = E + 2, so 7 + V = 15 + 2.
  2. V = 17 - 7 = 10.
  3. That fits a pentagonal prism: two pentagons and five rectangles.

The answer is 10.

Where students go wrong

Using Euler's formula on a cylinder, cone or sphere. Those have curved surfaces, not polygon faces, so F + V = E + 2 only applies to polyhedra.

Also called naming solids, 3D shapes, faces edges and vertices, prisms and pyramids or identifying solid figures.

What you can put on this worksheet

Name the solid
Give the most specific name for the solid. — a square pyramid → Square pyramid
Faces, edges and vertices
Find the number of faces, edges and vertices of this solid. — a triangular prism → F=5, E=9, V=6
Polyhedra, nets and cross-sections
A net has 6 squares. What solid does it fold into? → Cube
Euler's formula
A polyhedron has 5 faces and 9 edges. How many vertices does it have? → 6
Trapezoidal prisms and rectangular pyramids too
Give the most specific name for the solid. — a cube → Cube
Name the solid from its net
Give the most specific name for the solid this net folds into. — a net of a solid → Triangular pyramid

Questions about these worksheets

Yes. Every classifying solids sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Geometry is usually taken around 9th or 10th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the classifying solids questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 6: name the solid, faces, edges and vertices, polyhedra, nets and cross-sections, euler's formula, trapezoidal prisms and rectangular pyramids too and name the solid from its net. Tick as many as you want and set how many of each, or let it spread them evenly.

Naming a prism for its side faces instead of its base. Every prism has rectangles up the sides; a pentagonal prism is the one whose two ends are pentagons. The other slip is forgetting the hidden edges, drawn dashed, when counting.