ENGINEERING DRAWING- Polygon

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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