document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=273725>Question 273725</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how could i explain to a teacher how to find the area of a trapazoid? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #199939 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=199939\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> use the formula for a trapezoid.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that formula is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "area =  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28b1+%2B+b2%29%2F2%29+%2A+a ALIGN=MIDDLE  ALT=\"%28%28b1+%2B+b2%29%2F2%29+%2A+a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "b1 is the top base<BR>\n" );
document.write( "b2 is the bottom base<BR>\n" );
document.write( "a is the altitude (height) of the trapezoid.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "attached reference helps you to see how this works.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<a  rel=nofollow HREF= \"http://www.mathopenref.com/trapezoidarea.html\" target = \"_blank\">http://www.mathopenref.com/trapezoidarea.html</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "how the formula was derived is a lot more complicated.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if you look at the picture of a trapezoid shown below, you will see that the trapezoid is composed of a rectangle and a triangle on each end.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/problems/273725.jpg\" alt = \" ********** PICTURE NOT FOUND\" />\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The trapezoid in the picture is composed of the areas of 1+2+3.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2 is a rectangle.<BR>\n" );
document.write( "1 and 3 are triangles.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if you complete a larger rectangle, then you will see that the area of this larger rectangle is composed of the areas of 1+2+3+4+5.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The area of 2 is made by the base b1 * the altitude (a).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The area of 1+2+3+4+5 is made by the base b2 * the altitude (a).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The formula for the area of the trapezoid is a*(b1+b2)/2 which is the same as:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(a*b1)/2 + (a*b2)/2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "now a*b1 = the area called 2 which is the area of the smaller rectangle.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "now also a*b2 = the area of (1+2+3+4+5) which is the area of the larger rectangle.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "based on the previous 2 statements, the area of the trapezoid is equivalent to:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(2/2) + (1+2+3+4+5)/2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this is equivalent to:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the area of (2/2) + the area of (1/2) + (2/2) + (3/2) + (4/2) + (5/2)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "now (2/2) + (2/2) = 2 so our formula becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the area of 2 + the areas of (1/2) + (3/2) + (4/2) + (5/2)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "we also know that the area of triangle 4 is equivalent to the area of triangle 1.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "we also know that the area of triangle 5 is equivalent to the area of triangle 3.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This is because triangle 4 is congruent to triangle 1, and because triangle 5 is congruent to triangle 3.   These triangles are congruent by SSS.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "what this means is that we can substitute the area of triangle 1 for the area of triangle 4.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "what this also means that we can substitute the area of triangle 3 for the area of triangle 5.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "our formula of:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "area of 2 + areas of (1/2) + (3/2) + (4/2) + (5/2)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "can be made into:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "area of 2 + areas of (1/2) + (1/2) + (3/2) + (3/2)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this is because 1 and 4 are equivalent, and 3 and 5 are equivalent.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since 1/2 + 1/2 = 1, and since 3/2 + 3/2 = 3, our formula becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2 + 1 + 3.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if we reorder the terms, we get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1 + 2 + 3 which is the area of our trapezoid.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "by looking at each of the piece parts, we have determined that the area of the trapezoid given by the formula:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "area = a*(b1+b2)/2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "is equivalent to the formula:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "area = (a*b1)/2 + (a*b2)/2 which is the area of the smaller rectangle divided by 2 plus the area of the larger rectangle divided by 2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "it's tricky, but it works.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if you can't deal with the complexity of the derivation, then just stick with the formula.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the formula for the area of a trapezoid is equal to (b1+b2)/2 * a.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );