document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1137151>Question 1137151</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A frustum of a regular square pyramid has bases with sides of length 6 and 10. The height of the frustum is 12, find the surface area. </SPAN>\n" );
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document.write( "A frustum of a regular square pyramid has bases with sides of length 6 and 10. The height of the frustum is 12, find the surface area. \r<BR>\n" );
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document.write( "The areas of the two bases are easy: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E2+=+100 ALIGN=MIDDLE  ALT=\"10%5E2+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%5E2+=+36 ALIGN=MIDDLE  ALT=\"6%5E2+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To find the lateral surface area, you need to know the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slant+ ALIGN=MIDDLE  ALT=\"slant+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=height ALIGN=MIDDLE  ALT=\"height\"   DISABLED_style= \"max-width:90%; height:auto;\" > of each face.\r<BR>\n" );
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document.write( "To find that slant height, drop a perpendicular from the middle of one side of the top base to the bottom base.  \r<BR>\n" );
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document.write( "With the side lengths of the two bases <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" >, that perpendicular will touch the bottom base <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > units from the edge (half of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" >, minus half of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" >).  \r<BR>\n" );
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document.write( "Then, since the height of the frustum is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the slant height of each face, by the Pythagorean Theorem, is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2812%5E2%2B2%5E2%29+=+sqrt%28148%29+=+2%2Asqrt%2837%29 ALIGN=MIDDLE  ALT=\"sqrt%2812%5E2%2B2%5E2%29+=+sqrt%28148%29+=+2%2Asqrt%2837%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Each face is then a trapezoid with bases <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and height <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%2837%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt%2837%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >; that makes the area of each face <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2Asqrt%2837%29 ALIGN=MIDDLE  ALT=\"16%2Asqrt%2837%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So the total surface area, both bases and all four faces, is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100%2B36%2B4%2816%2Asqrt%2837%29%29+=+136%2B64%2Asqrt%2837%29 ALIGN=MIDDLE  ALT=\"100%2B36%2B4%2816%2Asqrt%2837%29%29+=+136%2B64%2Asqrt%2837%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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