Construction of Polygons

A. Construction of Regular Hexagon within a Circle of Side 4 cm:

Steps:

i. Draw a circle of radius equal to the length of the side of the hexagon.

ii. Draw the horizontal diameter AB.

iii. With centres A and B respectively, and radius of the circle, draw arcs above and below AB to cut the circumference at C, D, E and F.

iv. Join all the points to complete the Hexagon.

B. Construction of Regular Polygons Using Specific Methods:

1. Construction of a Hexagon using the 30°/60° Set Square.

Steps:

i. Draw a horizontal line and mark off AB = 100 mm.

ii. With the aid of the set square, draw lines and mark off C and D, in turn, = AB

iii. At C and D, use the set square to draw lines and mark off E and F =  AB.

iv. Join EF to complete the required Hexagon. Use bold lines to outline the drawing.

C. Construction of a Regular Hexagon given the Distance across Flats:

Here a circle is inscribed in a hexagon.

Distance of flats = diameter of circle.

Steps:

i. Draw a vertical and horizontal line that intersect.

ii. Draw a circle with centre O having a diameter equal to the distance across flats.

iii. Draw a horizontal line at the bottom of the circle.

iv. Draw tangents to the circle with the 60° set-square.

v. Draw a horizontal line at the top of the circle.

vi. Join the points of intersection of the tangents to produce the required hexagon. Use bold lines to outline the drawing.

D. Construction of a Regular Octagon given the Distance Across Corners:

Here a circle is circumscribed in an octagon so that the circle diameter defines the distance across the corners of the hexagon.

Steps:

i. Draw horizontal and vertical diameters AB and CD respectively.

ii. Draw a circle whose diameter is equal to the distance across the corners of the octagon.

iii. Draw Lines EF and GH, passing through the centre of the circle at 45°.

iv. Mark all the points the circle intersects with.

v. Draw lines through all the points to complete the required octagon.

E. Construction of a Regular Polygon Using General Method:

Steps:

i. Draw AB = given length of polygon (Let’s say 5 cm)

ii. Draw a Square, name it ABCD.

iii. Join points A & C.

iv. Take B as the centre and take the radius as AB, then draw an arc.

v. BisectBisect means dividing into two equal parts. It means to divide a geometric figure such as a line, an angle or any other shape into two congruent parts (or two parts... More the line AB and join the two points.

vi. Use the line you just drew and mark the points that touch AC and the arc as 4 and 6 as shown in the diagram below. Then Bisect the line “4,6”

vii. Join the points and mark the point that touches the horizontal line we drew earlier as 5.

viii. Use the length of “56” as the raidus and draw arcs which will be marked as 7, 8, and 9 as shown below.

ix. Take A5 as radius and 5 as centre, draw a circle.

x. With AB as radius, draw arcs on the circle, starting with A as centre and then B as centre.

xi. Draw all the arcs. Make sure the tip of the polygon touches the horizontal line above point 9. This is our second polygon with 5 sides which is a pentagon.

xii. Take A6 as radius, and 6 as centre, draw another circle.

xiii. With AB as radius, draw arcs on the circle, starting with A as centre and then B as centre. Then use the first two arcs as centres to draw two more arcs. The arcs must be equally spaced (i.e. same radius throughout)

xiv. Next, connect all the points to obtain a hexagon.

xv. Keep repeating the process with A7, and A8 as radius and 7 and 8 as centres. Draw circles, then use AB as the radius to draw arcs to inscribe a heptagon and octagon.

Let’s finally construct a nonagon, using radius A9 and 9 as centre to construct the circle. Then AB as the radius to draw arcs around the circle and then finally join all the points.

Note: We can also join Points A and B to point 6 to draw a triangle.

Technical Drawing Questions: