Wednesday 10 December 2014

How to construct a regular hexagon when its sides are given?

To understand the construction of a Regular Hexagon when its sides are given. Click on the link to Watch the VIDEO explanation: Watch Video


Construction of a Regular Hexagon Given the Sides.
A regular polygon has all its sides and all its angles equal. A regular hexagon can be constructed in two ways. Select the method by clicking on it.
Method 1
To construct a regular hexagon given side AB is equal to 3.2 cm
The steps of construction are as follows
Draw a circle of radius 3.2 cm
Take any point A on its circumference.
With the same radius of 3.2 cm, taking A as centre, cut the circle at B.
From B, with the same radius, cut the circle at C and so on until you obtain 6 points A, B, C , D, E and F.
Join AB, BC, CD, EF and AF.
Therefore, ABCDEF is the required hexagon.
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Method 2
In this method we construct the regular hexagon making use of the fact that it is made up of 6 equilateral triangles.
A regular hexagon subtends 360 degrees by 6 is equal to 60 degrees at the centre.
Triangle AOB  is an equilateral triangle.
Area of hexagon is equal to 6 into Area of triangle AOB
6 into root 3 by 4 into AB square
6 into root 3 by 4 into  3.2 whole square which is equal to 26.60 cm square.
Now proceed as stated with the construction
Draw AB is equal to 3.2 cm
With centres A and B and radius 3.2 cm, draw two arcs which intersect at O.
Notice that triangle AOB is one of the 6 equilateral triangles.
With centre O, the same radius of 3.2 cm cut the previous pair of arcs at C and F.
Join AF and BC
With centres C and F, and with the same radius of 3.2 cm, cut the previous arcs at D and E.
Join CD, DE and EF.
Therefore, ABCDEF is the regular hexagon.

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