document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=868046>Question 868046</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the surface area of a hexagonal prism with an apothem of 3 a height of 4 and a side being 2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #523523 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=523523\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Apothem is defined for regular polygons as the distance from a side to the center of the polygon.<BR>\n" );
document.write( "A regular hexagon with a side of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > has an apothem of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29 ALIGN=MIDDLE  ALT=\"sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >= approximately <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.732 ALIGN=MIDDLE  ALT=\"1.732\"   DISABLED_style= \"max-width:90%; height:auto;\" > . It could not have an apothem of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28330%2C300%2C-2.2%2C2.2%2C-2%2C2%2C%0D%0Arectangle%280%2C-1.732%2C0.1%2C-1.63%29%2C%0D%0Agreen%28triangle%280%2C0%2C0%2C-1.732%2C1%2C-1.732%29%29%2Carrow%281%2C-0.866%2C0%2C-0.866%29%2C%0D%0Atriangle%280%2C0%2C-1%2C-1.732%2C1%2C-1.732%29%2Ctriangle%280%2C0%2C-1%2C1.732%2C1%2C1.732%29%2C%0D%0Atriangle%280%2C0%2C-2%2C0%2C-1%2C-1.732%29%2Ctriangle%280%2C0%2C-2%2C0%2C-1%2C1.732%29%2C%0D%0Atriangle%280%2C0%2C2%2C0%2C1%2C-1.732%29%2Ctriangle%280%2C0%2C2%2C0%2C1%2C1.732%29%2C%0D%0Alocate%28-0.55%2C-1.5%2C1%29%2Clocate%280.45%2C-1.5%2C1%29%2C%0D%0Alocate%281.05%2C-.746%2Capothem%29%2Clocate%28-0.05%2C1.7%2C2%29%2C%0D%0Alocate%28-1.05%2C-0.05%2C2%29%2Clocate%28-1.5%2C0.86%2C2%29%2C%0D%0Alocate%280.55%2C0.93%2C2%29%2Clocate%28-0.5%2C1%2C2%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For a regular polygon, the area can be calculated as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28perimeter%29%28apothem%29%2F2 ALIGN=MIDDLE  ALT=\"%28perimeter%29%28apothem%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "A hexagon with a side of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > has a perimeter of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%29%282%29=12 ALIGN=MIDDLE  ALT=\"%286%29%282%29=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and a surface area of approximately <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%281.732%29%2F2=10.392 ALIGN=MIDDLE  ALT=\"12%281.732%29%2F2=10.392\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The lateral area of a right prism can be calculated as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28perimeter%29%28height%29 ALIGN=MIDDLE  ALT=\"%28perimeter%29%28height%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "A hexagonal base prism with a perimeter of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" > and a height of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "has a lateral area of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%284%29=48 ALIGN=MIDDLE  ALT=\"12%284%29=48\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Adding that lateral area plus the area of the two hexagonal bases, we get a total area of<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48%2B2%2810.392%29=48%2B10.784=68.784 ALIGN=MIDDLE  ALT=\"48%2B2%2810.392%29=48%2B10.784=68.784\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );