Where have I gone wrong?

Can you prove it? - A small exercise for your brain.


We all know area formula for various standards shapes, but have you ever wondered how these would have been derived or at least tried to verify it? I came across this thought while observing beautiful design works on the floor of a temple and tried my hands to find the area of somewhat bigger hexagon than the one shown below. You too try it out and post your finding in the comments section. Let us try to learn the basics, as basics are vital to start revolutions!!!!!!

Consider each  to be one 1 sq meter for our convenience and prove the area formulae for above hexagon.

So our hexagon has 3 on a side, and it is a regular hexagon. Regular hexagon is made up of 6 equilateral triangle and area formula for an equilateral triangle is (sqrt (3)/4)*(side) ^2. Hence our formula answer is 6*((sqrt (3)/4)*(side) ^2) = 23.38, but there are only 19 smaller hexagon. Could you identify where I have gone wrong in my calculation?

Example: Here you can see how formulae for calculating area of a square are verified.

Area formulae for square: (side) ^2. In above figure each side of the square consists 3 smaller hexagon, so according to area of square formula it amounts to be (3) ^ 2 = 9 smaller hexagons. If we count the number of hexagons in the above square it totals to 9. Thus the area formula for square has been verified.

In subsequent posts, let’s divert our attention on how these formulas were derived. Happy learning!!!