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Geometric figures

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;

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.

Quadrilaterals are also sometimes called quadrangles or tetragons.

 

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.

   

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.

 

 

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