# Types Of Polygons And Definitions Pdf

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The solid plane region, the bounding circuit, or the two together, may be called a polygon. The segments of a polygonal circuit are called its edges or sides , and the points where two edges meet are the polygon's vertices singular: vertex or corners. The interior of a solid polygon is sometimes called its body. An n -gon is a polygon with n sides; for example, a triangle is a 3-gon. A simple polygon is one which does not intersect itself.

## 6.2: Polygons

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

This means that there is some dispute as to whether an equilateral triangle is a special case of an isosceles triangle or not! 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! Some parallelograms have lines of symmetry depending on whether they are also squares, rectangles or rhombuses , but most do not. There are an infinite number of examples of different irregular polygons that could be shown, and only one example is given.

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. Crescent shapes are made when two circles overlap, or when one circle is removed from another circle. Please note that there is some disagreement over the definitions and properties of 3d shapes. Cones have either 1 or 2 faces, 0 or 1 edges, and 1 apex which is described by some mathematicians as a vertex. If the triangular faces making up the prism are all equilateral, then the shape is also called a Tetrahedron.

They are named after the Greek philosopher Plato who wrote about them in his philosophical discussions. A regular tetrahedron has equilateral triangles for its faces, and is one of the 5 platonic solids. A regular octahedron has equilateral triangles for its faces, and is one of the 5 platonic solids. A regular icosahedron is one of the 5 platonic solids with all faces being equilateral triangles. The sheets have been split up into US shapes and UK shapes, as there is a difference in the terminology used.

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.

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Home Search Site Online Practice. Seasonal Christmas Easter Halloween. 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. Quicklinks to According to Wikipedia: " In geometry, an isosceles triangle is a triangle that has two sides of equal length.

What is the interior angle of a regular pentagon? 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. 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 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 Cuboids have 6 faces, 12 edges and 8 vertices. All the faces on a cuboid are rectangular. Sphere Spheres have either 0 or 1 faces, 0 edges and 0 vertices. Ellipsoid Ellipsoids have either 0 or 1 faces, 0 edges and 0 vertices.

Cylinder Cylinders have either 2 or 3 faces, 0 or 2 edges, and 0 vertices. 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 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 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 Triangular-based pyramids have 4 faces, 6 edges and 4 vertices. The base is a triangle. All of the faces are triangular. 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 pyramids have 7 faces, 12 edges, and 7 vertices. The base is a hexagon. All of the other faces are triangular. 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.

There are only 5 platonic solids: Regular tetrahedron Cube or regular hexahedron Regular octahedron Regular dodecahedron Regular icosahedron. Tetrahedron A Tetrahedrons is the same as a triangular pyramid. They have 4 triangular faces, 6 edges and 4 vertices. Cube regular hexahedron Cubes have 6 faces, 12 edges and 8 vertices. A cube is a type of cuboid and is one of the 5 platonic solids. Octahedron Octahedrons are a shape with 8 faces, 12 edges and 6 vertices.

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

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. 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. Using these sheets will help your child to: know different geometric formula; apply a range of formula to solve problems.

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## Know the names and properties of polygons

Regular polygon:. A polygon which has all its sides of equal length and all its angles of equal measures is called a regular polygon. Examples of regular polygon:. In the adjoining figure of an equilateral triangle ABC there are three sides i. Therefore, an equilateral triangle is a regular polygon. In the adjoining figure of a square ABCD there are four sides i. Therefore, a square is a regular polygon.

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. Here are our list of 2d geometric shapes, including triangles, quadrilaterals and polygons. 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. This means that there is some dispute as to whether an equilateral triangle is a special case of an isosceles triangle or not! 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!

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Developments in Spatial Data Handling pp Cite as. Spatial models are often based on polygons both in 2D and 3D. In this paper we discuss the relevant aspects related to polygons in these standards and compare several implementations. A quite exhaustive set of test polygons with holes has been developed. The test results reveal significant differences in the implementations, which causes interoperability problems.

These segments are called its edges or sides , and the points where two edges meet are the polygon's vertices or corners. The interior of the polygon is sometimes called its body. A polygon is a 2-dimensional example of the more general polytope in any number of dimensions. Today a polygon is more usually understood in terms of sides.

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* Джабба, дело очень серьезное.*

### 2 Comments

Let us discuss them one by one. Regular Polygon. In a regular polygon, all the sides of the polygon are equal, and all the interior angles are the same. Irregular Polygon. A polygon with an irregular shape. Convex Polygon. Concave Polygon. Trigons. Quadrilateral Polygon. Pentagon Polygon. Hexagons.

A regular polygon has all sides equal and all angles equal. An irregular polygon is not regular. A convex polygon has no reflex angles. A concave polygon has at least one reflex angle (an angle larger than °).