# Hexagon

GinoJ
Posers and Puzzles 20 Feb '07 19:41
1. 20 Feb '07 19:41
One of the sides of a regular hexagon is 1cm. Find the area of the hexagon.

Show your work.
2. 20 Feb '07 19:58
Originally posted by GinoJ
One of the sides of a regular hexagon is 1cm. Find the area of the hexagon.

Show your work.
A regular hexagon with each side = 1 cm consist of 6 equilateral triangles with sides 1 cm. Each triangle have an area of sqrt(3)/4 = 0.43 giving the hexagon an area of 6 * sqrt(3)/4 = 2.60

Near enough?
3. 20 Feb '07 20:051 edit
Originally posted by FabianFnas
A regular hexagon with each side = 1 cm consist of 6 equilateral triangles with sides 1 cm. Each triangle have an area of sqrt(3)/4 = 0.43 giving the hexagon an area of 6 * sqrt(3)/4 = 2.60

Near enough?
The answer is a "natural number" if I must give a clue. Il also has an extremely short solution.
4. 20 Feb '07 20:16
Really? 'Natural' as in 'Positive Integer'? Are we that close to a revolution in euclidian geometry then?
5. 20 Feb '07 20:171 edit
Originally posted by Mephisto2
Really? 'Natural' as in 'Positive Integer'? Are we that close to a revolution in euclidian geometry then?
0,1,2,3,4,5,6,7,8,9 etc...

 Eliminate 0. ðŸ˜›

So, another clue: It's a positive integer.
6. 20 Feb '07 20:26
The very simple solution is expressed as a positive integer number of cm²?
7. PBE6
Bananarama
20 Feb '07 20:281 edit
Originally posted by GinoJ
0,1,2,3,4,5,6,7,8,9 etc...

 Eliminate 0. ðŸ˜›

So, another clue: It's a positive integer.
There's no chance it's a positive integer. The area is (3/2)*SQRT(3), as reported (rounded) above. No matter how many times you multiply an irrational number by a rational one (other than 0 of course), you'll never get a positive integer.
8. 20 Feb '07 20:332 edits
La solution est:

1.5a
a*a=3
9. 20 Feb '07 20:411 edit
Originally posted by FabianFnas
A regular hexagon with each side = 1 cm consist of 6 equilateral triangles with sides 1 cm. Each triangle have an area of sqrt(3)/4 = 0.43 giving the hexagon an area of 6 * sqrt(3)/4 = 2.60

Near enough?
This is correct, I'm not quite sure why GinoJ thinks that it's not. Perhaps, Gino, you can show us your idea? According to what I'm learning at school, Fabian gave a fully correct answer. That is the way how this exercise should be solved. Perhaps you didn't mean a hexagon but a polygon with different number of sides.
10. 20 Feb '07 20:46
Originally posted by GinoJ
OK, then.

1.5a
a*a=3
So, '1.5a' is a positive integer a.k.a. 'natural number'? You make me feel sorry about myself to even want to read this forum anymore.
11. 20 Feb '07 20:46
Originally posted by kbaumen
This is correct, I'm not quite sure why GinoJ thinks that it's not. Perhaps, Gino, you can show us your idea? According to what I'm learning at school, Fabian gave a fully correct answer. That is the way how this exercise should be solved. Perhaps you didn't mean a hexagon but a polygon with different number of sides.
Are you blind?
12. 20 Feb '07 20:47
Originally posted by Mephisto2
So, '1.5a' is a positive integer a.k.a. 'natural number'? You make me feel sorry about myself to even want to read this forum anymore.
I was tricking you guys. ðŸ˜€
13. 20 Feb '07 21:03
Originally posted by GinoJ
I was tricking you guys. ðŸ˜€
Don't try, Gino, Explain your natural answer, or what your flaw in your reasoning...

Don't "I was tricking you" me... ðŸ˜
14. 20 Feb '07 21:05
Originally posted by FabianFnas
Don't try, Gino, Explain your natural answer, or what your flaw in your reasoning...

Don't "I was tricking you" me... ðŸ˜
Ok, sire.
15. 20 Feb '07 21:103 edits
Hey Fabian, thank God I am bein' soft G.