document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1025449>Question 1025449</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the total cost of polishing , if it cost 10 php per square meter to polish the lateral surface area of a 10 meter marble monument in the shape of a frustum of a regular pyramid with upper and lower base edges measuring 8 m and 4 m, respectively. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #640872 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=640872\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> All length measurements will be in meters, and all surface area measurements will be in square meters, but I will not write the units except at the end.<BR>\n" );
document.write( "The cross-section of that pyramid and frustum would look like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28200%2C440%2C-5%2C5%2C-1%2C21%2C%0D%0Agreen%28triangle%28-4%2C0%2C0%2C0%2C0%2C20%29%29%2C%0D%0Agreen%28triangle%284%2C0%2C0%2C0%2C0%2C20%29%29%2C%0D%0Agreen%28rectangle%280%2C0%2C-0.5%2C0.5%29%29%2C%0D%0Aline%28-2%2C10%2C2%2C10%29%2Cline%28-4%2C0%2C4%2C0%29%2C%0D%0Aline%28-4%2C0%2C-2%2C10%29%2Cline%284%2C0%2C2%2C10%29%2C%0D%0Alocate%28-2%2C0%2C4%29%2Clocate%282%2C0%2C4%29%2Clocate%280.1%2C6%2C10%29%2C%0D%0Alocate%28-1%2C10%2C2%29%2Clocate%281%2C10%2C2%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > with similar triangles <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28200%2C440%2C-5%2C5%2C-1%2C21%2C%0D%0Agreen%28triangle%28-4%2C0%2C0%2C0%2C0%2C20%29%29%2Cgreen%28triangle%28-2%2C10%2C0%2C10%2C0%2C20%29%29%2C%0D%0Agreen%28triangle%281%2C10%2C3%2C10%2C3%2C20%29%29%2C%0D%0Agreen%28rectangle%283%2C10%2C2.5%2C10.5%29%29%2Cgreen%28rectangle%280%2C0%2C-0.5%2C0.5%29%29%2C%0D%0Alocate%28-2%2C0%2C4%29%2Clocate%283.1%2C15.5%2C10%29%2C%0D%0Alocate%280.1%2C15.5%2C10%29%2Clocate%280.1%2C5.5%2C10%29%2C%0D%0Alocate%28-1%2C10%2C2%29%2Clocate%281%2C10%2C2%29%2C%0D%0Alocate%28-3%2C5%2Cx%29%2Clocate%28-1%2C15%2Cx%29%2Clocate%282%2C15%2Cx%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The large right triangle has the same angle measures,<BR>\n" );
document.write( "and twice the base (4 rather than 2), compared to the smaller right triangle.<BR>\n" );
document.write( "So, the height of the large right triangle is twice the height of the smaller one,<BR>\n" );
document.write( "meaning that the height of the frustrum (10) and the height of the small triangle are both half of the height of the large triangle ( <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A10=20 ALIGN=MIDDLE  ALT=\"2%2A10=20\"   DISABLED_style= \"max-width:90%; height:auto;\" > ).<BR>\n" );
document.write( " <BR>\n" );
document.write( "In the large right triangle, the Pythagorean theorem says that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%29%5E2=4%5E2%2B20%5E2 ALIGN=MIDDLE  ALT=\"%282x%29%5E2=4%5E2%2B20%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%29%5E2=16%2B400 ALIGN=MIDDLE  ALT=\"%282x%29%5E2=16%2B400\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%29%5E2=416 ALIGN=MIDDLE  ALT=\"%282x%29%5E2=416\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=sqrt%28416%29 ALIGN=MIDDLE  ALT=\"2x=sqrt%28416%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the slant height of the pyramid.<BR>\n" );
document.write( "The lateral faces of pyramid and frustrum look like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28200%2C460%2C-5%2C5%2C-1%2C22%2C%0D%0Agreen%28triangle%28-4%2C0%2C0%2C0%2C0%2C20.4%29%29%2C%0D%0Agreen%28triangle%284%2C0%2C0%2C0%2C0%2C20.4%29%29%2C%0D%0Agreen%28rectangle%280%2C0%2C-0.5%2C0.5%29%29%2C%0D%0Alocate%28-2%2C0%2C4%29%2Clocate%282%2C0%2C4%29%2C%0D%0Alocate%280.1%2C11%2C20%29%2Clocate%28-2.1%2C9%2Csqrt%28416%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28200%2C260%2C-5%2C5%2C-1%2C12%2C%0D%0Aline%28-4%2C0%2C4%2C0%29%2Cline%28-2%2C10.2%2C2%2C10.2%29%2C%0D%0Aline%28-4%2C0%2C-2%2C10.2%29%2Cline%284%2C0%2C2%2C10.2%29%2C%0D%0Aline%280%2C0%2C0%2C10.2%29%2Crectangle%280%2C0%2C0.5%2C0.5%29%2C%0D%0Alocate%28-2%2C0%2C4%29%2Clocate%282%2C0%2C4%29%2Clocate%280.1%2C6%2Csqrt%28416%29%2F2%29%2C%0D%0Alocate%28-1%2C10.2%2C2%29%2Clocate%281%2C10.2%2C2%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The surface area of each of the lateral faces of the frustum can be calculated as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%288%2B4%29%2F2%29%2A%28sqrt%28416%29%2F2%29 ALIGN=MIDDLE  ALT=\"%28%288%2B4%29%2F2%29%2A%28sqrt%28416%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The total lateral surface area can be calculated as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A%28%288%2B4%29%2F2%29%2A%28sqrt%28416%29%2F2%29=12sqrt%28416%29 ALIGN=MIDDLE  ALT=\"4%2A%28%288%2B4%29%2F2%29%2A%28sqrt%28416%29%2F2%29=12sqrt%28416%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "At 10 php per square meter, the cost for polishing the lateral surface would be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2A12%2Asqrt%28416%29=%22approx.%22 ALIGN=MIDDLE  ALT=\"10%2A12%2Asqrt%28416%29=%22approx.%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28247.53php%29 ALIGN=MIDDLE  ALT=\"highlight%28247.53php%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );