List of Geometric Shapes

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.

Along with each shape, we have also included the properties of each shape and other helpful information.

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.

Is an Equilateral triangle a special case of an Isosceles triangle?

According to Wikipedia:

" In geometry, an isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having two and only two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case. "

Source: https://en.wikipedia.org/wiki/Isosceles_triangle

This means that there is some dispute as to whether an equilateral triangle is a special case of an isosceles triangle or not!

Most modern textbooks include use the 'at least' definition for isosceles triangles.

List of Geometric Shapes - Quadrilaterals

A quadrilateral is a polygon with 4 sides.

Quadrilaterals are also sometimes called quadrangles or tetragons.

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.

Convex and Concave Polygons

Polygons can be concave or convex in their shape.

Convex shapes have all angles less than 180°

Concave shapes have at least one reflex angle greater than 180°

Triangles are always convex.

Convex hexagon

convex hexagon

Convex shapes have no reflex angles (angles > 180° )

Concave hexagon

concave hexagon

Concave shapes have at least one reflex angle greater than 180°

Convex pentagon

convex pentagon

Concave pentagon

concave pentagon

Convex octagon

convex octagon

Concave octagon

concave octagon

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).

Regular shapes are always convex.

Irregular shapes can be concave or convex.

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

REGULAR SHAPES

IRREGULAR SHAPES

Equilateral Triangle

equilateral triangle angles

Sides: 3

Angle: 60°

Interior angles add up to 180°

Irregular Triangle

irregular shapes triangle

Square

regular shapes square

Sides: 4

Angle: 90°

Interior angles add up to 360°

Irregular Quadrilateral

irregular quadrilateral

Pentagon

2d shapes regular pentagon

Sides: 5

Angle: 108°

Interior angles add up to 540°

Irregular Pentagon

irregular pentagon

Hexagon

shapes for kids regular hexagon

Sides: 6

Angle: 120°

Interior angles add up to 720°

Irregular Hexagon

list of geometric shapes irregular hexagon

Heptagon

regular heptagon

Sides: 7

Angle: 128.6° (to 1dp)

Interior angles add up to 900°

Irregular Heptagon

geometric shapes irregular heptagon

Octagon

2d shape regular octagon

Sides: 8

Angle: 135°

Interior angles add up to 1080°

Irregular Octagon

geometric shapes irregular octagon

Nonagon

2 dimensional shapes regular nonagon

Sides: 9

Angle: 140°

Interior angles add up to 1260°

Irregular Nonagon

irregular nonagon

Decagon

regular shapes decagon

Sides: 10

Angle: 144°

Interior angles add up to 1440°

Irregular Decagon

shapes for kids irregular decagon

Hendecagon

regular shapes hendecagon

Sides: 11

Angle: 147.3° (to 1dp)

Interior angles add up to 1620°

Irregular Hendecagon

irregular hendecagon

Dodecagon

regular shapes dodecagon

Sides: 12

Angle: 150°

Interior angles add up to 1800°

Irregular Dodecagon

irregular dodecagon

Formula for Interior Angles of a Polygon

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

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

Interior Angle of a regular polygon = total of interior angles / number of sides

Example

What is the interior angle of a regular pentagon?

Step 1) Total of interior angles is 180 x (number of sides - 2)

= 180 x (5 - 2) = 180 x 3 = 540 °

Step 2) The interior angle = total of interior angles ÷ number of sides = 540 ÷ 5 = 108 °

Answer: 108 °

List of Geometric Shapes - Curved 2d Shapes

Here are some curved 2d shapes which have not yet been included.

Circle

list of geoemtric shapes circle



Circles have a point in the centre from which each point on the diameter is equidistant.

They have infinite lines of symmetry.

How many sides does a circle have?

This is an interesting question - the answer could be 0 (no straight sides), 1 curved side, or an infinite number of sides are all possible answers.

Ellipse

list of geoemtric shapes ellipse



Ellipses are like circles which have been squashed or stretched.

They have 2 lines of symmetry.

They are also a special type of oval.

The longest and shortest diameters of the ellipse are called the major and minor axes.

These axes are also the lines of symmetry.

Crescent

list of geoemtric shapes crescent



Crescent shapes are made when two circles overlap, or when one circle is removed from another circle .

The perimeter of crescents are made from two circular arcs.

They have 1 line of symmetry.

Our moon forms crescent shapes during its phases.

Some countries such as Turkey or Algeria have crescent shapes on their flags.

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.

Please note that there is some disagreement over the definitions and properties of 3d shapes.

Some mathematicians allow a face to be curved and some do not.

Some mathematicians allow an edge to be curved and some do not.

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 either 0 or 1 faces, 0 edges and 0 vertices.

Ellipsoid

3d geometric shapes ellipsoid

Ellipsoids have either 0 or 1 faces, 0 edges and 0 vertices.

Cylinder

list of geometric shapes cylinder

Cylinders have either 2 or 3 faces, 0 or 2 edges, and 0 vertices.

Cone

shapes for kids cone

Cones have either 1 or 2 faces, 0 or 1 edges, 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 Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

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.

Parts of a Circle Worksheets and Support

Do you know the special geometric names to describe the different parts of a circle?

Well you can find all the support you need on this page, complete with some practice worksheets and an online quiz!

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.
 

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