# POLYGON

Polygon is a plane figure bounded by many (usually five or more) straight lines.

When all the sides and included angles are equal, it is called as a **REGULAR POLYGON.**

When all the sides and included angles are unequal, it is called **IRREGULAR POLYGON.**

Polygons are named in terms of their number of sides as given below:

S. No. |
NAME |
NUMBER OF SIDES |

a | PENTAGON | 5 |

b | HEXAGON | 6 |

c | HEPTAGON | 7 |

d | OCTAGON | 8 |

e | NONAGON | 9 |

f | DECAGON | 10 |

g | UNDECAGON | 11 |

h | DUODECAGON | 12 |

### PROPERTIES OF POLYGON:

- All corners of a regular polygon lie on the circle. The sides of a regular polygon will be tangential to the circle drawn in side.

- The sum of the interior angles of a polygon is equal to (2 x n – 4) x right angle, where n is the number of sides.

- The sum of exterior angles of a polygon is equal to 360°.

- The sum of the interior angle and the corresponding external angle is 180°.

### Draw a regular heptagon of side 25 mm.

**Semi-circular method **

- Draw a line AB equal to 25 mm.

- Extend BA to a convenient length.

- `A’ as centre and radius AB describe a semi-circle.

- Divide the semi-circle into seven equal parts (number of sides) using divider.

- Number the points as 1,2,3,4,5,6 starting from `P’.

- Join A2

- Draw the perpendicular bisectors from 2A and AB intersecting at 0.

- `0′ as centre and OA or OB as radius describe a circle.

- Mark the points C,D,E,F and 2 on the circle such that BC = CD = DE = EF = F2 = AB.

- Join the line BC, CD, DE, EF and F2.

- ABCDEF2 is required heptagon.

**Semi-circle method**

Follow the procedure upto dividing the semi-circle into number of equal parts.

- Join A2.

- Join A3, A4, A5 and A6 and extend to a convenient length.

- With centre `B’ and radius AB draw an arc cutting A6 extended line at `C’.

- `C’ as centre and same radius, draw an arc cutting the line A5 at `D’.

- Locate the points E & F in the same manner.

- Join BC, CD, DE, EF and F2.

- ABCDEF2 is the required heptagon.

### Draw a Pentagon inside a circle of diameter 60 mm.

- Draw the line AH equals to 60 mm. (Diameter of circle).

- `O’ as centre OA as radius describe a circle.

- Divide AH into 5 equal parts (as many equal parts as the sides).

- A and H as centres, AH as radius describe arcs intersecting at `P’.

- Join P2 and extend it to meet the circle at `B’.

- Set off BC, CD, DE, EF equals to AB on the circle.

- Join the points.

- ABCDEF is the required pentagon.

### Draw a Hexagon (Circumscribing) of side 32 mm by Arc Method.

- Draw a circle of radius 32 mm.

- Mark the diameter AD.

- With same radius, A and D as centres. draw two arcs cutting the circle at points B,F,E & C respectively.

- Join AB, BC, CD, DE, EF and FA.

- ABCDE is the required hexagon.

### Draw a Hexagon inside a circle of diameter 60 mm (inscribing).

- Draw a line FC equal to 60 mm (Diameter of circle).

- ‘O’ as centre describe a circle on the diameter FC.

- F as centre FO as radius draw an arc at A.

- ‘A’ as centre, same radius draw an arc at B.

- In the same manner set the points C,D & E.

- Join AB, BC, CD, DE, EF and FA.

- ABCDEF is the required hexagon.

### Draw a Hexagon with Across Flat Method.

Hexagon, distance across flat of 45 mm

- Draw a circle of Φ 45. (45 mm is the size across flat).

- Draw two horizontal tangents BC and FE.

- With 60° setsquare draw four tangents, touching the horizontal tangents.

- Mark the corners A,B,C,D,E and F.

- ABCDEF is the required hexagon.

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