# 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.
• 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.