The following procedures describe the methods of drawing regular polygons of any number of sides.
METHOD 1:
Q.construct a regular polygon of any number of sides (say pentagon) given the length of one of its sides as 25 mm.
Solution:
Procedure:
AB is the given side. It is required to draw a regular polygon. For example, say, it is required to draw a pentagon. Proceed AB to P such that ABBP. With B as centre and radius AB, draw a semi-circle, and by trial and error, divide it into number of equal arcs equal to the number of sides of the polygon. In this case, divide into five equal arcs because it is a pentagon, and number the division points as 1, 2, 3 etc., as shown in Fig. Connect B to the second division. For any polygon, irrespective of the number of sides always connect B to the second division. Draw the bisectors for AB and B2 to intersect each other at O. With O as centre and radius OA, draw a circle. Now with AB as radius, cut the circle at C, D and E to get the other points of the polygon. Connect CD, DE and get the required polygon.
METHOD-2 :
To construct a regular polygon of any number sides, given the length of one of its side
Procedure:
AB is the given side. It is required to draw a polygon, for example, say octagon. Draw AB, the given side and construct the square ABPQ. Connect diagonal AP. With B as centre and radius AB, draw are arc. Draw the perpendicular bisector of AB, to intersect the diagonal AP at 4 and the arc at 6. It is evident that if a circle is drawn with 4 as centre and radius 4-A, it will pass through corners A, B, P and Q of the square. Now corners A, B, P with 6 as centre and radius 6A draw circle. With AB as radius, cut this circle successively to obtain a hexagon. Suppose if a pentagon (not shown in Fig. ) is to be constructed, bisect-4-6′ at 5. Now 5 centre and radius 5A, draw a circle, successively cut with Al as radius to get a pentagon. With 6 as centre and radius 45, cut the perpendicular bisector of AB at 7. With 7 as centre and with the same radius, cut the bisector of AB at 8. Similarly obtain the points 9, 10 etc., To construct an heptagon, draw a circle with 7 as centre and 7A as radius. Cut this circle with AB as radius, successively and complete the polygon. To construct the required octagon, with 8 as centre and radius 8A, draw a circle and with 8-B as radius, successively cut the circle at C, D, E, F, G, and H and by connecting them complete the required polygon.
