List of Geometric Shapes

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Welcome to the Math Salamanders' Geometric Shapes Information Page.

Here you will find a list of different geometric shapes to help you to identify a range of 2d and 3d shapes.

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List of Geometric Shapes

Here you will find our list of different Geometric shapes. There is a 2d shape area followed by a 3d shape area.

There is an image of each shape, as well as the properties that the shape has. Using these sheets will help your child to:
  • know the properties of different 2d & 3d shapes;
  • recognise different 2d & 3d shapes;
  • know the interior angles of regular polygons;
All the Math sheets in this section follow the Elementary Math Benchmarks.

2d Geometric Shapes

Here are our list of 2d geometric shapes, including triangles, quadrilaterals and polygons

List of Geometric Shapes - Triangles

Equilateral Triangle

geometric shapes equilateral triangle



Equilateral triangles have all angles equal to 60°, and all sides equal length.

All equilateral triangles have 3 lines of symmetry.

Isoscles Triangle

Isosceles triangle



Isosceles triangles have 2 angles equal and 2 sides of equal length.

All isosceles triangles have a line of symmetry.

Scalene Triangle

scalene triangle



Scalene triangles have no angles equal, and no sides of equal length.

Right Triangle

right triangle or right angled triangle



Right triangles (or right angled triangles) have one right angle (equal to 90°).

Obtuse Triangle

obtuse triangle



Obtuse triangles have one obtuse angle (an angle greater than 90°). The other two angles are acute (less than 90°).

Acute Triangle

acute triangle



Acute triangles have all angles acute.

List of Geometric Shapes - Quadrilaterals

A quadrilateral is a polygon with 4 sides.

There are quite a few members of the quadrilateral family. There are also some members which are a subset of other members of this family!
See below if this confuses you!

Square

list of geoemtric shapes square



Squares have 4 equal sides and 4 right angles.

They have 4 lines of symmetry.

All squares belong to the rectangle family.

All squares belong to the rhombus family.

All squares are also parallelograms.

Rectangle

list of geometric shapes rectangle



Rectangles have 4 sides and 4 right angles.

They all have 2 lines of symmetry (4 lines if they are also a square!)

All rectangles belong to the parallelogram family.

Rhombus

list of geometric shapes rhombus



Rhombuses (rhombii) have 4 equal sides.

Both pairs of opposite sides are parallel.

They all have 2 lines of symmetry (4 lines if they are a square!)

All rhombuses belong to the parallelogram family.

Parallelogram

list of geometric shapes parallelogram



Parallelograms have 2 pairs of parallel sides.

Some parallelograms have lines of symmetry (depending on whether they are also squares, rectangles or rhombuses), but most do not.

Trapezoid US
(Trapezium UK)

quadrilateral family trapezium



Trapezoids US (Trapeziums UK) have one pair of parallel sides.

Some trapezoids have a line of symmetry.

Please note the differences between the definitions for US and UK.

Kite

quadrilateral family kite



Kites have 2 pairs of equal sides which are adjacent to each other.

Trapezium US
(Trapezoid UK)

Trapezium US



Trapeziums US (Trapezoids UK) are quadrilaterals with no parallel sides.

Please note the differences between the definitions for US and UK.

Regular and Irregular Polygons

Here is a list of regular polygons from 3 to 10 sides.

For each polygon, a regular and an irregular example have been shown.

Any regular shape will be mathematically similar to the example shown (having the same angles).

There are an infinite number of examples of different irregular polygons that could be shown, and only one example is given.

Equilateral Triangle

equilateral triangle angles

Angle: 60°

Interior angles add up to 180°

Irregular Triangle

irregular shapes triangle

Square

regular shapes square

Angle: 90°

Interior angles add up to 360°

Irregular Quadrilateral

irregular quadrilateral

Pentagon

2d shapes regular pentagon

Angle: 108°

Interior angles add up to 540°

Irregular Pentagon

irregular pentagon

Hexagon

shapes for kids regular hexagon

Angle: 120°

Interior angles add up to 720°

Irregular Hexagon

list of geometric shapes irregular hexagon

Heptagon

regular heptagon

Angle: 128.6°

Interior angles add up to 900°

Irregular Heptagon

geometric shapes irregular heptagon

Octagon

2d shape regular octagon

Angle: 135°

Interior angles add up to 1080°

Irregular Octagon

geometric shapes irregular octagon

Nonagon

2 dimensional shapes regular nonagon

Angle: 140°

Interior angles add up to 1260°

Irregular Nonagon

irregular nonagon

Decagon

regular shapes decagon

Angle: 144°

Interior angles add up to 1440°

Irregular Decagon

shapes for kids irregular decagon

The formulae for the interior angles of a polygon are as follows:

Total of interior angles = 180 x (number of sides - 2)

Angle = total of interior angles / number of sides



List of Geometrics Shapes - 3D Shapes

Here are some common 3D shapes that you should know.

Along with a picture of each shape, the number of faces, edges and vertices are also given.

Common properties of the 3D shapes are also given.

Cube

3 d shapes cube

Cubes have 6 faces, 12 edges and 8 vertices.

All sides on a cube are equal length.

All faces are square in shape.

A cube is a type of cuboid.

Cuboid

3 d shapes cuboid

Cuboids have 6 faces, 12 edges and 8 vertices.

All the faces on a cuboid are rectangular.

Sphere

3d geometric shapes sphere

Spheres have 1 curved face, 0 edges and 0 vertices.

Cylinder

list of geometric shapes cylinder

Closed Cylinders have 3 faces, 2 edges and 0 vertices.

Closed cylinders have 2 circular or elliptical faces and one curved rectangular face.

Cone

shapes for kids cone

Cones have 2 faces, 1 edge and 1 apex (which is described by some mathematicians as a vertex).

Triangular Prism

triangular prism

Triangular Prisms have 5 faces, 9 edges, and 6 vertices.

The two faces at either end are triangles, and the rest of the faces are rectangular.

Hexagonal Prism

hexagonal prism

Hexagonal Prisms have 8 faces, 18 edges, and 12 vertices.

The two faces at either end are hexagons, and the rest of the faces are rectangular.

Triangular-based Pyramid

printable 3d shapes triangular based pyramid

Triangular-based pyramids have 4 faces, 6 edges and 4 vertices.

The base is a triangle. All of the faces are triangular.

If the triangular faces making up the prism are all equilateral, then the shape is also called a Tetrahedron.

Square-based Pyramid

3d geometric shapes square based pyramid

Square based pyramids have 5 faces, 8 edges and 5 vertices

The base is a square. All the other faces are triangular.

Hexagonal Pyramid

hexagonal pyramid

Hexagonal pyramids have 7 faces, 12 edges, and 7 vertices.

The base is a hexagon. All of the other faces are triangular.

The 5 Platonic Solids

The platonic solids form a set of 5 polyhedra with the following special properties:

  • the faces of the platonic solids have to be regular and congruent.
  • the same number of faces meet at each vertex.

They are named after the Greek philosopher Plato who wrote about them in his philosophical discussions.

There are only 5 platonic solids:

  • Regular tetrahedron
  • Cube or regular hexahedron
  • Regular octahedron
  • Regular dodecahedron
  • Regular icosahedron

Tetrahedron

tetrahedron

A Tetrahedrons is the same as a triangular pyramid.

They have 4 triangular faces, 6 edges and 4 vertices.

A regular tetrahedron has equilateral triangles for its faces, and is one of the 5 platonic solids.

Cube (regular hexahedron)

3 d shapes cube

Cubes have 6 faces, 12 edges and 8 vertices.

All sides on a cube are equal length.

All faces are square in shape.

A cube is a type of cuboid and is one of the 5 platonic solids.

Octahedron

3 d shapes octahedron

Octahedrons are a shape with 8 faces, 12 edges and 6 vertices.

A regular octahedron has equilateral triangles for its faces, and is one of the 5 platonic solids.

Dodecahedron

printable 3d shapes dodecahedron

Dodecahedrons are a shape with 12 faces, 30 edges and 20 vertices.

A regular dodecahedron has regular pentagons for its faces, and is one of the 5 platonic solids.

Icosahedron

printable 3d shapes icosahedron

Icosahedron are a shape with 20 faces, 30 edges and 12 vertices.

All the faces are triangles.

A regular icosahedron is one of the 5 platonic solids with all faces being equilateral triangles.

Printable List of Geometric Shapes 2D

Here you will some printable 2d shape sheets showing a range of 2d shapes.

You can choose to have the properties of the 2d shapes displayed or not.

The sheets have been split up into US shapes and UK shapes, as there is a difference in the terminology used.

Printable Geometric Shapes 3D

Here you will some printable 3 d shape sheets showing a range of 3d shapes.

You can choose to have the sheet printed in color or black.

More Printable Shape Sheets - 2D & 3D Shape Sheets

Here you will find a selection of printable 2d and 3d shape sheets.

Each sheet is available in color or black and white, and labelled or unlabelled.

Using these sheets will help your child to:

  • recognise and name a range of 2d and 3d shapes;
  • recognise regular and irregular shapes.
All the free printable shape sheets in this section support Elementary Math benchmarks.

Geometry Formula Sheet

Here you will find our support page about different Geometry formulas, including formulas about triangles, circles, quadrilaterals and polygons, as well as 3d shape formulae.

In the Geometry Cheat Sheet section you will find a range of printable geometry sheets with formula and information about angles, 2d and 3d shapes.

Using these sheets will help your child to:

  • know different geometric formula;
  • apply a range of formula to solve problems.
All the Math sheets in this section follow the Elementary Math Benchmarks.
 

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