document.write( "Question 1142265: Seven pencils are held together in hexagon shape by an elastic band. If the pencils are of diameter 7mm, what is the length of the band in this shape \n" ); document.write( "
Algebra.Com's Answer #762962 by ikleyn(52943)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "            In my solution, I assume that all pencils have hexagonal section.\r
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document.write( "As soon as you make a sketch to the problem, the solution will come into your mind instantly.\r\n" );
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document.write( "The band has the form of a polygon with 12 sides.\r\n" );
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document.write( "Six of these 12 sides have the length equal to the length of the side of a section of the pencil, which is half of its diameter,\r\n" );
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document.write( "i.e. 3.5 mm.\r\n" );
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document.write( "Six other sides have the length  \"3.5%2Asqrt%283%29\" mm.\r\n" );
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document.write( "Thus the length of the elastic band is equal to the perimeter of this 12-gon\r\n" );
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document.write( "    P = \"6%2A3.5+%2B+6%2A3.5%2Asqrt%283%29\" = \"%286%2A3.5%29%2A%281+%2B+sqrt%283%29%29\" = \"21%2A%281+%2B+sqrt%283%29%29\" = 57.37 mm (approximatyely, correct with two decimal places).\r\n" );
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\n" ); document.write( "\n" ); document.write( "For other configurations with cylindrical pencils,  I solved similar problems  LONG  TIME  AGO  at this forum.\r
\n" ); document.write( "\n" ); document.write( "If you are interested,  look into the links\r
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\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/Rectangles/Rectangles.faq.question.1089992.html\r
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\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/Polygons/Polygons.faq.question.1116600.html\r
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\n" ); document.write( "\n" ); document.write( "in the archive to this forum.\r
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\n" ); document.write( "\n" ); document.write( "By the way, the tutor Alan fairly noted to you, that your formulation in this post is not perfect.\r
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\n" ); document.write( "\n" ); document.write( "I totally agree with him.\r
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\n" ); document.write( "\n" ); document.write( "Therefore, there is a great sense to you to look on how similar problems were formulated under these links\r
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