List of Geometric Shapes

$List of Geometric Shapes Salamander holding ball$

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.

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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.

Quicklinks to ...

Triangles
Quadrilaterals
Concave & Convex Polygons
Regular & Irregular Polygons
Curved 2d Shapes
3d Shapes
Platonic Solids
Printable Shape Sheets

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.

$list of geometric shapes 2d$

$printable geometric shapes 2d noinfo$

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.

$3 d shapes list of geometric shapes 3d info$

$printable shapes list of geometric shapes 3d$

$3 d shapes list of geometric shapes 3d blank$

$shapes clipart list of geometric shapes 3d bw$

$shapes for kids list of geometric shapes 3d col$

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.

$printable shapes 2d image$ $printable shapes 3d image$

Printable Shapes - 2D and 3D Shape Sheets

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!

$Parts of a circle worksheet image$

Parts of a Circle Worksheets

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: