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Maths Fun(?)
#873397
03/12/13 02:18 PM
03/12/13 02:18 PM
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Joined: Nov 2004
Posts: 21,889 Bucks, England
Urban Worrier
OP
True Blue Boomer
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OP
True Blue Boomer
Joined: Nov 2004
Posts: 21,889
Bucks, England
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-1. Draw a regular hexagon then draw the six "alternate" vertices. (Skip one vertex - 1 to 3, 2 to 4 etc). If the area of the original hexagon is 6, what is the area of the internal hexagon that is formed?
-2. Inscribe a square in a circle of radius R. Draw an arc from one corner of the square with radius equal to the side of the square. The area formed between this arc and the circle is a crescent. Find the area of this crescent in terms of R. -3. In the equations below, replace each letter with a number from 1 to 9, using each number only once: a/b + c/12 = 1 1/12 d/e + 5/f = 7/8 g/h + 3/i = 1 1/2
To waste one second of one's life is a betrayal of one's self. I wonder what's on television...?
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Re: Maths Fun(?)
[Re: Urban Worrier]
#873586
03/13/13 11:21 AM
03/13/13 11:21 AM
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Joined: Nov 2000
Posts: 18,719 Ottawa Ontario Canada
CanukDenis
Graduate Boomer
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Graduate Boomer
Joined: Nov 2000
Posts: 18,719
Ottawa Ontario Canada
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1. Draw a regular hexagon then draw the six "alternate" vertices. (Skip one vertex - 1 to 3, 2 to 4 etc). If the area of the original hexagon is 6, what is the area of the internal hexagon that is formed?
So I don't have to type "sqrt(3)"!): u = sqrt(3) v = 1/u (ratio radii outer:inner)
R = outer radius Pentagon area: 3u(R^2) / 2
Given: area = 6 ; soooooo: 3u(R^2) / 2 = 6 R = sqrt(4 / u) : ~1.5196....
r = inner radius r = R * v : ~.8773.... area = 3u(r^2)/2 area = (drum rolls!) 2 exactement.
I'm a man of few words, BUT I use 'em often!!
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Re: Maths Fun(?)
[Re: Urban Worrier]
#873654
03/13/13 06:30 PM
03/13/13 06:30 PM
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Joined: Nov 2004
Posts: 21,889 Bucks, England
Urban Worrier
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True Blue Boomer
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OP
True Blue Boomer
Joined: Nov 2004
Posts: 21,889
Bucks, England
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CCb - very nice! Denis - good solve. It can be done by similar triangles. The inner hexagon contains 6 identically-sized equilateral triangles and the outer hexagon contains these 6 plus 6 more plus 12 halves for a total of 18 triangles. Thus, the area of the outer hexagon is 3 times the area of the inner one. manxman - if I read your answer correcly (one over 2 R-squared) then we beg to differ. What's your working?
To waste one second of one's life is a betrayal of one's self. I wonder what's on television...?
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Re: Maths Fun(?)
[Re: Urban Worrier]
#873701
03/13/13 11:45 PM
03/13/13 11:45 PM
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Joined: Jul 2002
Posts: 29,125 Unionville
manxman
Sonic Boomer
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Sonic Boomer
Joined: Jul 2002
Posts: 29,125
Unionville
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Sorry, checked my work over and got R^2
Last edited by manxman; 03/14/13 07:32 AM.
Sometimes lost is where you need to be. Just because you don't know your direction doesn't mean you don't have one.
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