Math Problem - Tilted Forum Project Discussion Community

BlitzkriegKommt · 11-21-2004, 11:22 AM

Last week I entered a math competition and one of their questions was. There is a hexagon with each side with length of 5 cm. What is the total length of all of its diagonal. I was really put off by this question, but then I thought that diagonals would cut each other and make 90 degree angles each.
Then I know one side is 5 cm, and its a 90 degree angle, so it'd be like 45 45 90 triangles, in which the ratio is 1, 1, square root of two respectively.
Doing then all the proportion and math, i got 15 multiplied by square root of two or approximately 21.213 Is there any math expert out there who can verify my answer, help is appreciated

Thank you. Hope it all makes sense.

fckm · 11-21-2004, 11:40 AM

not quite. for the diagonals that radiate from the center, they make angles of 60 degrees (360/6). there are other diagonals that don't go through the center. I believe there are a total of nine diagonals

BlitzkriegKommt · 11-21-2004, 04:14 PM

Yeah, I see that now. Well I got that wrong.
So how would anyone solve that?

11-21-2004, 04:30 PM

Split the hexagon into triangles, and then use pythagoras to work out the angles and distances.

welshbyte · 11-23-2004, 06:00 PM

I havent done trigonometry for over 3 years.. lets see if it stuck...

lengthOfDiagType1 = 5 / (sin 120) = 5.7735 (From sin 120 = 5 / Hypoteneuse)
lengthOfDiagType2 = 2 * sideLength = 2 * 5 = 10

count(diagType1) = 6
count(diagType2) = 3

(6 * lengthOfDiagType1) + (3 * lengthOfDiagType2) = 64.641 cm (to 3 dp)

Could someone check that please, its very possible that i got it wrong hehe.

No pythagoras here zen_tom

P.S. sorry i listed it like a program, thats just what i'm good at...

FngKestrel · 11-23-2004, 06:06 PM

Practical solution:
Get 7 rulers.
Take 6 of the 7 rulers, construct a hexagon with side length 5cm.
Take the 7th ruler, measure the diagonals and add them up.

BlitzkriegKommt · 12-02-2004, 09:01 PM

Thanks Welshbyte, hope I had done that.
FngKestrel, heh next time I'll ask them for a ruler.

keldon · 12-02-2004, 10:56 PM

I get a different answer than welshbyte. The "long" diagonals are indeed 10cm long, but for the shorter ones I get 5*sqrt(3) or ~8.66.

I get this answer from the Law on Sines: x/sin(120) = 5/sin(30).

The total length would be 3*10 + 6*(5*sqrt(3)), or ~81.96.

11-21-2004, 11:22 AM	#1 (permalink)
BlitzkriegKommt Upright Location: Houston	Math Problem Last week I entered a math competition and one of their questions was. There is a hexagon with each side with length of 5 cm. What is the total length of all of its diagonal. I was really put off by this question, but then I thought that diagonals would cut each other and make 90 degree angles each. Then I know one side is 5 cm, and its a 90 degree angle, so it'd be like 45 45 90 triangles, in which the ratio is 1, 1, square root of two respectively. Doing then all the proportion and math, i got 15 multiplied by square root of two or approximately 21.213 Is there any math expert out there who can verify my answer, help is appreciated Thank you. Hope it all makes sense.

11-21-2004, 11:40 AM	#2 (permalink)
fckm Insane Location: Ithaca, New York	not quite. for the diagonals that radiate from the center, they make angles of 60 degrees (360/6). there are other diagonals that don't go through the center. I believe there are a total of nine diagonals __________________ And if you say to me tomorrow, oh what fun it all would be. Then what's to stop us, pretty baby. But What Is And What Should Never Be.

11-23-2004, 06:00 PM	#5 (permalink)
welshbyte Insane Location: Wales, UK, Europe, Earth, Milky Way, Universe	I havent done trigonometry for over 3 years.. lets see if it stuck... lengthOfDiagType1 = 5 / (sin 120) = 5.7735 (From sin 120 = 5 / Hypoteneuse) lengthOfDiagType2 = 2 * sideLength = 2 * 5 = 10 count(diagType1) = 6 count(diagType2) = 3 (6 * lengthOfDiagType1) + (3 * lengthOfDiagType2) = 64.641 cm (to 3 dp) Could someone check that please, its very possible that i got it wrong hehe. No pythagoras here zen_tom P.S. sorry i listed it like a program, thats just what i'm good at... __________________ There are only two industries that refer to their customers as "users". - Edward Tufte

11-21-2004, 04:14 PM	#3 (permalink)
BlitzkriegKommt Upright Location: Houston	Yeah, I see that now. Well I got that wrong. So how would anyone solve that?

11-21-2004, 04:30 PM	#4 (permalink)
zen_tom Guest	Split the hexagon into triangles, and then use pythagoras to work out the angles and distances.

11-23-2004, 06:06 PM	#6 (permalink)
FngKestrel Junkie	Practical solution: Get 7 rulers. Take 6 of the 7 rulers, construct a hexagon with side length 5cm. Take the 7th ruler, measure the diagonals and add them up.

12-02-2004, 09:01 PM	#7 (permalink)
BlitzkriegKommt Upright Location: Houston	Thanks Welshbyte, hope I had done that. FngKestrel, heh next time I'll ask them for a ruler.

12-02-2004, 10:56 PM	#8 (permalink)
keldon Upright	I get a different answer than welshbyte. The "long" diagonals are indeed 10cm long, but for the shorter ones I get 5sqrt(3) or ~8.66. I get this answer from the Law on Sines: x/sin(120) = 5/sin(30). The total length would be 310 + 6(5sqrt(3)), or ~81.96.