document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=966755>Question 966755</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this problem :\r<BR>\n" );
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document.write( "  A regular quadrilateral pyramid has a base side 16 cm and 6 cm height. Find the total area.\r<BR>\n" );
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document.write( "Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #590886 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52786)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=590886\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <TABLE >\n" );
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document.write( "A sketch of your pyramid is schematically shown in the &nbsp;<B>Figure 1a</B>&nbsp; (not in the scale, though). \r<BR>\n" );
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document.write( "The base of the given pyramid is a square, &nbsp;of course. \r<BR>\n" );
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document.write( "Draw the straight interval from the base center to the middle of the base side. \r<BR>\n" );
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document.write( "Its length is &nbsp;16/2 = 8 cm. \r<BR>\n" );
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document.write( "Next, &nbsp;draw the slant height from the vertex of the pyramid to that point &nbsp;(<B>Figure 1b</B>).\r<BR>\n" );
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document.write( "Find the length of the slant height from the right triangle. &nbsp;It is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5Bslant%5D ALIGN=MIDDLE  ALT=\"h%5Bslant%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%286%5E2+%2B+8%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%286%5E2+%2B+8%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2836+%2B+64%29 ALIGN=MIDDLE  ALT=\"sqrt%2836+%2B+64%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28100%29 ALIGN=MIDDLE  ALT=\"sqrt%28100%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm ALIGN=MIDDLE  ALT=\"cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Notice that the slant height has the same length for all lateral faces of the pyramid.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+220%2C+200%2C++-2.5%2C+3.5%2C+-0.5%2C+3.8%2C+%0D%0A%0D%0A++++++++++++line+%28++0.0%2C+0.0%2C++3.0%2C++0.0%29%2C%0D%0A++++++++++++line+%28++0.0%2C+0.0%2C+-2.0%2C++0.8%29%2C%0D%0A++++++green%28line+%28+-2.0%2C+0.8%2C++1.0%2C++0.8%29%29%2C%0D%0A++++++green%28line+%28++1.0%2C+0.8%2C++3.0%2C++0.0%29%29%2C%0D%0A%0D%0A++++++++++++line+%28++0.0%2C+0.0%2C++0.5%2C++3.4%29%2C%0D%0A++++++++++++line+%28++3.0%2C+0.0%2C++0.5%2C++3.4%29%2C%0D%0A++++++green%28line+%28++1.0%2C+0.8%2C++0.5%2C++3.4%29%29%2C%0D%0A++++++++++++line+%28+-2.0%2C+0.8%2C++0.5%2C++3.4%29%2C%0D%0A%0D%0A++++++++red%28line+%28+0.5%2C++3.4%2C++0.5%2C++0.4%29%29%2C%0D%0A%0D%0A++++++++++locate+%28+1.0%2C++0.0%2C+16%29%2C%0D%0A++++++++++locate+%28-1.6%2C++0.5%2C+16%29%2C%0D%0A++++++red%28locate+%28+0.54%2C+1.7%2C+6%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<B>Figure 1a</B>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<B>Figure 1b</B>\r<BR>\n" );
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document.write( "Now, &nbsp;the area of each triangular lateral face is &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2A10 ALIGN=MIDDLE  ALT=\"16%2A10\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=80 ALIGN=MIDDLE  ALT=\"80\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm%5E2 ALIGN=MIDDLE  ALT=\"cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Hence, &nbsp;the lateral area of the pyramid is four times this value, &nbsp;i.e. &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A80 ALIGN=MIDDLE  ALT=\"4%2A80\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=320 ALIGN=MIDDLE  ALT=\"320\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm%5E2 ALIGN=MIDDLE  ALT=\"cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "To get the total surface area of the pyramid, &nbsp;you need to add the area of the base square, &nbsp;which is &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%5E2 ALIGN=MIDDLE  ALT=\"16%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=256 ALIGN=MIDDLE  ALT=\"256\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm%5E2 ALIGN=MIDDLE  ALT=\"cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<B>Answer</B>. &nbsp;The lateral surface area of the pyramid is &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=320 ALIGN=MIDDLE  ALT=\"320\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm%5E2 ALIGN=MIDDLE  ALT=\"cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The total surface area of the pyramid is &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=320 ALIGN=MIDDLE  ALT=\"320\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=256 ALIGN=MIDDLE  ALT=\"256\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=576 ALIGN=MIDDLE  ALT=\"576\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm%5E2 ALIGN=MIDDLE  ALT=\"cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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