document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1074800>Question 1074800</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let ABCDEFGH be a rectangular prism, as shown, where AB = 2, AD = 3, and AE = 5. Find the volume of pyramid ACFH.\r<BR>\n" );
document.write( "\n" );
document.write( "https://latex.artofproblemsolving.com/0/a/3/0a3404805162de58ee7c86ac6b0e5d23327c0026.png </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #689539 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5345)</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=689539\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The drawing looks (sort of) like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28350%2C300%2C-2%2C33%2C-2%2C28%2C%0D%0Agreen%28triangle%280%2C8%2C31%2C8%2C20%2C14%29%29%2C%0D%0Agreen%28triangle%2820%2C26%2C31%2C8%2C20%2C14%29%29%2C%0D%0Agreen%28triangle%280%2C8%2C20%2C26%2C20%2C14%29%29%2C%0D%0Atriangle%280%2C8%2C11%2C0%2C11%2C12%29%2Ctriangle%2831%2C8%2C11%2C0%2C11%2C12%29%2C%0D%0Atriangle%280%2C8%2C0%2C20%2C11%2C12%29%2Ctriangle%2831%2C8%2C31%2C20%2C11%2C12%29%2C%0D%0Atriangle%2820%2C26%2C0%2C20%2C11%2C12%29%2Ctriangle%2820%2C26%2C31%2C20%2C11%2C12%29%2C%0D%0Alocate%28-1%2C8%2CA%29%2Clocate%2831.2%2C8%2CH%29%2Clocate%2819.5%2C14%2CE%29%2C%0D%0Alocate%28-1%2C21%2CB%29%2Clocate%2831.2%2C21%2CG%29%2Clocate%2819.5%2C27.3%2CF%29%2C%0D%0Alocate%2810.5%2C13.6%2CC%29%2Clocate%2810.5%2C0%2CD%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "The prism has the diagonals of all its 6 faces marked.<BR>\n" );
document.write( "Those diagonals split each rectangular face of the prism into two congruent right triangles,<BR>\n" );
document.write( "with each of those triangles being half of a rectangular face of the prism.\r<BR>\n" );
document.write( "\n" );
document.write( "Slicing along those diagonals,<BR>\n" );
document.write( "they cut off 4 pyramids out of 4 corners of the prism,<BR>\n" );
document.write( "to leave pyramid ACFH.<BR>\n" );
document.write( "The volume of each of the pyramids cut off is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6 ALIGN=MIDDLE  ALT=\"1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the volume of the prism.<BR>\n" );
document.write( "After removing <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%281%2F6%29=2%2F3 ALIGN=MIDDLE  ALT=\"4%281%2F6%29=2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the volume of the prism,<BR>\n" );
document.write( "they are left with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-2%2F3=1%2F3 ALIGN=MIDDLE  ALT=\"1-2%2F3=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the volume of the prism.<BR>\n" );
document.write( "Since the volume of the prism (in cubic units) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A3%2A5 ALIGN=MIDDLE  ALT=\"2%2A3%2A5\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "the volume left (the volume of ACFH) is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A3%2A5%2F3=2%2A5=highlight%2810%29 ALIGN=MIDDLE  ALT=\"2%2A3%2A5%2F3=2%2A5=highlight%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );