document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1062175>Question 1062175</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Been struggling with this one,\r<BR>\n" );
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document.write( "Jack renovating his kitchen and has decided to use tiles on his counter-top which is 83cm by 203cm. The tiles are octagonal and square in a pattern where four octagons around one square. The square tiles are 3cm along one side.<BR>\n" );
document.write( "(a) Estimate the number of tiles they will need to cover the counter-top.<BR>\n" );
document.write( "(b) Each square tile costs $0.55 and each octagonal tile costs $0.78. Estimate the cost of the tiles to cover the counter-top.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #677169 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=677169\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I assume that we have regular octagon tiles<BR>\n" );
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document.write( "area of square = 3 * 3 = 9 cm^2<BR>\n" );
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document.write( "the octagon is a square with the corners cut off, each corner is a 45 - 45 -90 right triangle<BR>\n" );
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document.write( "the hypotenuse is 3cm, then calculate the length of a side<BR>\n" );
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document.write( "s^2 + s^2 = 3^2<BR>\n" );
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document.write( "2s^2 = 3^2<BR>\n" );
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document.write( "s = square root(3^2 / 2) = 3 / square root(2) = 1.5 * square root (2)<BR>\n" );
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document.write( "length of the octagon square = ( 3 + 2 * ( 1.5 * square root (2) )<BR>\n" );
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document.write( "area of octagon square = ( 3 + 3 *square root (2) )^2 = 9 + 18 * square root(2) + 18 = 27 + 18 * square root(2)<BR>\n" );
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document.write( "area of triangles = 4 * ( (1/2) * (3/2)square root(2) * (3/2)square root(2) ) = 9<BR>\n" );
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document.write( "area of octagon = 27 + 18square root(2) - 9 = 18(1 + square root(2)) = 43.46 cm^2<BR>\n" );
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document.write( "area of counter-top = 83 * 203 = 16849 cm^2<BR>\n" );
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document.write( "The area of the square and 4 octagon system = 9 + 4 * 43.46  = 182.84<BR>\n" );
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document.write( "There are 16849 / 182.84 = 92.2 approximately 92 systems<BR>\n" );
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document.write( "There are 92 squares and 4 * 92 = 368 octagons<BR>\n" );
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document.write( "Total cost = 92 * 0.55 + 368 * 0.78 = $337.64<BR>\n" );
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