document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=964200>Question 964200</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How to calculate the relative amounts of colour needed for a diamond shape?\r<BR>\n" );
document.write( "\n" );
document.write( "As part of our assignment we have to create our own design for a quilt and I choose to do a diamond, but I need to calculate the amount of colour I would need but I do not know how to do it. \r<BR>\n" );
document.write( "\n" );
document.write( "The functions that I have used to create the outer diamond are:<BR>\n" );
document.write( "y=x+15  (-15< x <0)<BR>\n" );
document.write( "y=-x-15 (-15< x <0)<BR>\n" );
document.write( "y=x-15  (0< x <15)<BR>\n" );
document.write( "y=-x+15 (0< x <15)\r<BR>\n" );
document.write( "\n" );
document.write( "These functions are for the inner diamond:<BR>\n" );
document.write( "y=x+10 (-10< x <0)<BR>\n" );
document.write( "y=x-10 (0< x <10)<BR>\n" );
document.write( "y=-5/5x+10 (0< x <10)<BR>\n" );
document.write( "y=-5/5x-10 (-10< x <0) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #589340 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=589340\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I would think that by<BR>\n" );
document.write( "y=-5/5x+10 you mean <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%285%2F5%29x%2B10 ALIGN=MIDDLE  ALT=\"y=-%285%2F5%29x%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" > , or simply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x%2B10 ALIGN=MIDDLE  ALT=\"y=-x%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and that by<BR>\n" );
document.write( "y=-5/5x-10 you mean <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%285%2F5%29x-10 ALIGN=MIDDLE  ALT=\"y=-%285%2F5%29x-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > , or simply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x-10 ALIGN=MIDDLE  ALT=\"y=-x-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Those equations make a design like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-16%2C16%2C-16%2C16%2C%0D%0Agrid%281%29%2Cblue%28line%28-15%2C0%2C0%2C15%29%29%2Cblue%28line%2815%2C0%2C0%2C15%29%29%2C%0D%0Ablue%28line%28-15%2C0%2C0%2C-15%29%29%2Cblue%28line%2815%2C0%2C0%2C-15%29%29%2C%0D%0Agreen%28line%28-10%2C0%2C0%2C10%29%29%2Cgreen%28line%2810%2C0%2C0%2C10%29%29%2C%0D%0Agreen%28line%28-10%2C0%2C0%2C-10%29%29%2Cgreen%28line%2810%2C0%2C0%2C-10%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > showing nested diamonds (or really nested squares).<BR>\n" );
document.write( "If calculating areas was necessary, we know that the area of a rhombus is half the product of the diagonal lengths.<BR>\n" );
document.write( "So, the area of the large square is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%2A30%2A30=450 ALIGN=MIDDLE  ALT=\"%281%2F2%29%2A30%2A30=450\"   DISABLED_style= \"max-width:90%; height:auto;\" > square units,<BR>\n" );
document.write( "and the area of the smaller square is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%2A20%2A20=200 ALIGN=MIDDLE  ALT=\"%281%2F2%29%2A20%2A20=200\"   DISABLED_style= \"max-width:90%; height:auto;\" > square units.<BR>\n" );
document.write( "We could invoke a lot of higher math, but not even the calculation of areas above is necessary to find the ratio of the areas.<BR>\n" );
document.write( " <BR>\n" );
document.write( "I appreciate your effort at using math to describe the design.<BR>\n" );
document.write( "without that (or a picture) I would have no idea of what your design was.<BR>\n" );
document.write( "The description was complicated, but the calculation is very simple,<BR>\n" );
document.write( "as in fifth grade math.<BR>\n" );
document.write( " <BR>\n" );
document.write( "The smaller, inside square's diagonals are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > as long as<BR>\n" );
document.write( "the larger, outside square's diagonals.<BR>\n" );
document.write( "The inside square is a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > scaled-down version of the outside one.<BR>\n" );
document.write( "Its inside square's sides are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > the length of the outside square's sides,<BR>\n" );
document.write( "and as a consequence, the inside square's area is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29%282%2F3%29=4%2F9 ALIGN=MIDDLE  ALT=\"%282%2F3%29%282%2F3%29=4%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > the area of the outside square.<BR>\n" );
document.write( " <BR>\n" );
document.write( "If you are going to cut squares in two sizes and sew one on top of another,<BR>\n" );
document.write( "for every 9 feet of material for the larger square you will need 4 feet of material for the smaller square.<BR>\n" );
document.write( " <BR>\n" );
document.write( "If, however, you are going to saw 4 trapezoids of the outside color,<BR>\n" );
document.write( "forming a frame around the inside square,<BR>\n" );
document.write( "that frame will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-4%2F9=9%2F9-4%2F9=blue%285%2F9%29 ALIGN=MIDDLE  ALT=\"1-4%2F9=9%2F9-4%2F9=blue%285%2F9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the area of the large outside square,<BR>\n" );
document.write( "and since the smaller inside square has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%284%2F9%29 ALIGN=MIDDLE  ALT=\"green%284%2F9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the area of the large outside square,<BR>\n" );
document.write( "so the ratio of visible material areas is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=blue%285%29%3Agreen%284%29 ALIGN=MIDDLE  ALT=\"blue%285%29%3Agreen%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > in favor of the outside color. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );