A regular octagon is **a closed shape with sides of equal length and interior angles of the same measurement**. It has eight symmetric lines and a rotational equilibrium of order 8. The interior angle at each vertex of a regular octagon is 135°. The central angle is 45°.

**Introducing polygons**

- Draw a regular pentagon and an irregular pentagon on the board.
- Get your students to count the sides and corners.
- Ask if the sides are the same length on both shapes.
- Emphasize that shapes with 5 sides are pentagons, but if the sides and corners are not equal it is an irregular pentagon.

To find the angle of any regular polygon you find the number of sides , which in this example is . You then subtract from the number of sides yielding . Take and multiply it by degrees to yield a total number of degrees in the regular nonagon. Then to find one individual angle we divide by the total number of angles .

In geometry, a polygon can be defined as **a flat or plane, two-dimensional closed shape bounded with straight sides**. It does not have curved sides. The sides of a polygon are also called its edges. The points where two sides meet are the vertices (or corners) of a polygon.

**A concave polygon is a polygon that is not convex**. . An example of a non-simple (self-intersecting) polygon is a star polygon. A concave polygon must have at least four sides.

five

**Polygons cannot contain any curved sides**, or holes. For example, a square is a polygon but a circle is not. is a closed, flat shape that has only straight sides. Polygons can have any number of sides and angles, but the sides cannot be curved.

**The rectangular-shaped screen of your laptop, television, or mobile phone** is an example of a polygon. A rectangular football pitch or playground is an example of a polygon. The Bermuda Triangle, which is a triangular shape, is a polygon. The Pyramids of Egypt are also an example of polygons (triangular)

The parts of polygons include **the sides, interior angles and exterior angles**. There is also the vertex, the spot where two sides meet, and the diagonals, or lines connecting vertices.

Regular megagon

In geometry, **a hexagon** can be defined as a polygon with six sides. The two-dimensional shape has 6 sides, 6 vertices and 6 angles.

Triangles, quadrilaterals, pentagons, and hexagons are all examples of polygons. The name tells you how many sides the shape has. For example, a triangle has three sides, and a quadrilateral has four sides.

Definition of a Polygon.

Shape | # of Sides |
---|---|

Octagon | 8 |

Nonagon | 9 |

Decagon | 10 |

n-gon | n sides |

**A regular polygon has equal length sides with equal angles between each side**. Any other polygon is an irregular polygon, which by definition has unequal length sides and unequal angles between sides. Circles and shapes that include curves are not polygons - a polygon, by definition, is made up of straight lines.

**Identify the below sets that show the polygon is arranged in the decreasing sequence of the number of sides.**

- Octagon, hexagon, pentagon, and quadrilateral.
- Pentagon, hexagon, octagon, and quadrilateral.
- Quadrilateral, pentagon, hexagon, and octagon.
- Hexagon, pentagon, quadrilateral, and octagon.

We can identify a polygon by checking the following characteristics in a shape: It is a closed shape, that is, there is no end that is left open in the shape. It ends and begins at the same point. It is a plane shape, that is, the shape is made of line segments or straight lines.

To draw a polygon, start by drawing a circle on a piece of paper using a protractor. Then, decide how many sides you want your polygon to have. Once you've decided, divide 360 by the number of sides to find out what the angle between each set of neighboring lines should be.

Area of a regular polygon formulas**area = n * a * ri / 2** , having ri - incircle radius (it's also an apothem - a line segment from the center to the midpoint of one of its sides) area = perimeter * ri / 2 , given ri and polygon perimeter.

Examples of Pentagons**The famous U.S. department of defense building in Washington D.C.** (The Pentagon building) The home plate on a baseball field. School crossing signs. Sections on a soccer ball.

To calculate the number of sides of the polygon, **divide 360 by the amount of the exterior angle**. For example, if the exterior angle is 60 degrees, then dividing 360 by 60 equals 6, which is the number of sides the polygon has.

In geometry, a **hendecagon (also undecagon or endecagon) or 11-gon** is an eleven-sided polygon. (The name hendecagon, from Greek hendeka "eleven" and –gon "corner", is often preferred to the hybrid undecagon, whose first part is formed from Latin undecim "eleven".)

A polygon can be defined as **a flat or plane, two-dimensional closed shape with straight sides**. It does not have curved sides. Polygons can be of two types: Regular Polygons – Polygons that have equal sides and angles are regular polygons.

Dated : 26-May-2022

Category : Education