document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1104881>Question 1104881</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the figure given below, triangle BAC is inscribed in a semi circle with BC = 73. Semi circles are constructed outside the triangle, with diameter AB = 48 and AC = 55. Find the area of the shaded region inside the two smaller semi circles but outside the larger circle.\r<BR>\n" );
document.write( "\n" );
document.write( "http://www.smartlearning.in/new_stsquestion.php?QuestionID=73640&page=1<BR>\n" );
document.write( "(please disregard the measurements given in the figure (3 cm and 4 cm) and follow whats stated on the word problem above)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #719601 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=719601\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You could calculate the shaded area as<BR>\n" );
document.write( "the sum of the areas of the two small semicircles,<BR>\n" );
document.write( "minus the ate of the large semicircle,<BR>\n" );
document.write( "plus the area of the triangle.<BR>\n" );
document.write( "The area of the triangle is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=base%2Aheight%2F2=55%2A48%2F2=1320 ALIGN=MIDDLE  ALT=\"base%2Aheight%2F2=55%2A48%2F2=1320\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "because AB and AC are perpendicular,<BR>\n" );
document.write( "so we can take one as the base of the triangle,<BR>\n" );
document.write( "and the other one would be the height.<BR>\n" );
document.write( "We could calculate the areas of the semicircles,<BR>\n" );
document.write( "but we do not need to, because we know ABC is a right triangle.<BR>\n" );
document.write( "The Pythagorean theorem says that the sum of<BR>\n" );
document.write( "the areas of the squares built on the legs of a right triangle<BR>\n" );
document.write( "are equal to the area of the square built on the hypotenuse.<BR>\n" );
document.write( "It works for semicircles too,<BR>\n" );
document.write( "so as you add the areas of the two smaller semicircles,<BR>\n" );
document.write( "you get the area of the large one,<BR>\n" );
document.write( "and when you subtract it you get zero,<BR>\n" );
document.write( "Just before you add the area of the triangle.<BR>\n" );
document.write( "In the end, the shaded area is equal to the area of the triangle:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%281320%29 ALIGN=MIDDLE  ALT=\"highlight%281320%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > area units.<BR>\n" );
document.write( "If you have to show your work,<BR>\n" );
document.write( "and the teacher insists on calculating the area of the semicircles,<BR>\n" );
document.write( "the area of a circle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2Aradius%5E2=pi%2Adiameter%5E2%2F4 ALIGN=MIDDLE  ALT=\"pi%2Aradius%5E2=pi%2Adiameter%5E2%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So, the area of a semicircle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2Adiameter%5E2%2F8 ALIGN=MIDDLE  ALT=\"pi%2Adiameter%5E2%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "For the small semicircles the areas are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A48%5E2%2F8 ALIGN=MIDDLE  ALT=\"pi%2A48%5E2%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A55%5E2%2F8 ALIGN=MIDDLE  ALT=\"pi%2A55%5E2%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "For the large semicircles, the area is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A73%5E2%2F8 ALIGN=MIDDLE  ALT=\"pi%2A73%5E2%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The area of the shaded region is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A48%5E2%2F8%2Bpi%2A55%5E2%2F8-pi%2A73%5E2%2F8%2B1320=%28pi%2F8%29%2A%2848%5E2%2B55%5E2-73%5E2%29%2B1320=%28pi%2F8%29%2A0%2B1320=1320 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Of course, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48%5E2%2B55%5E2=73%5E2 ALIGN=MIDDLE  ALT=\"48%5E2%2B55%5E2=73%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > , because ABC is a right triangle. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );