document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207323>Question 1207323</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For a ballet production, a truncated pyramid is constructed with a square base of 10 meters on a side, a height of 8 meters and a summit height of 2 meters. What is the total area of the surfaces of the truncated pyramid? </SPAN>\n" );
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document.write( "The problem as stated is nonsense, since we don't know what \"summit height\" of 2 meters is.<br><BR>\n" );
document.write( "It is a good problem if we assume that the 2 meters is supposed to be the length of a side of the square top of the truncated pyramid.  So I'll go ahead with that assumption.<br><BR>\n" );
document.write( "Consider the pyramid before it was truncated.<br><BR>\n" );
document.write( "Use similar triangles and the given dimensions to determine that the height of the original pyramid was 10m.<br><BR>\n" );
document.write( "The slant height of a face of the original pyramid (peak to midpoint of a side of the base) is the hypotenuse of a right triangle with legs 5m and 10m:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=sqrt%285%5E2%2B10%5E2%29=sqrt%28125%29=5sqrt%285%29 ALIGN=MIDDLE  ALT=\"h=sqrt%285%5E2%2B10%5E2%29=sqrt%28125%29=5sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The area of each triangular face of the original pyramid is (one-half base times height)<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%281%2F2%29%2810%29%285sqrt%285%29%29=25sqrt%285%29 ALIGN=MIDDLE  ALT=\"A=%281%2F2%29%2810%29%285sqrt%285%29%29=25sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The area of each face of the small pyramid that was cut off to form the truncated pyramid is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2B%281%2F2%29%282%29%28sqrt%285%29%29=sqrt%285%29 ALIGN=MIDDLE  ALT=\"A%2B%281%2F2%29%282%29%28sqrt%285%29%29=sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "So the area of each face of the truncated pyramid is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25sqrt%285%29-sqrt%285%29=24sqrt%285%29 ALIGN=MIDDLE  ALT=\"25sqrt%285%29-sqrt%285%29=24sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The total surface area of the truncated pyramid is the area of the two bases, plus the area of the four faces:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28100%2B4%29%2B4%2824sqrt%285%29%29=104%2B96sqrt%285%29 ALIGN=MIDDLE  ALT=\"%28100%2B4%29%2B4%2824sqrt%285%29%29=104%2B96sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=104%2B96sqrt%285%29 ALIGN=MIDDLE  ALT=\"104%2B96sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > square meters<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );