document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1210155>Question 1210155</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ABCE is a Parallelogram. ADEF is a Rhombus. Find the area of the composite figure.<BR>\n" );
document.write( "https://ibb.co/Jj2jKPD3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #851415 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=851415\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Absolutely! Let's break down this problem step-by-step.\r<BR>\n" );
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document.write( "**1. Finding the area of Rhombus ADEF**\r<BR>\n" );
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document.write( "* **Properties of a Rhombus:**<BR>\n" );
document.write( "    * All sides are equal.<BR>\n" );
document.write( "    * Diagonals bisect each other at right angles.<BR>\n" );
document.write( "* **Given:**<BR>\n" );
document.write( "    * EF = 17 (side of the rhombus)<BR>\n" );
document.write( "    * FO = 5 (half of diagonal FD)<BR>\n" );
document.write( "* **Finding EO:**<BR>\n" );
document.write( "    * Since triangle EOF is a right-angled triangle, we can use the Pythagorean theorem: $EF^2 = EO^2 + FO^2$<BR>\n" );
document.write( "    * $17^2 = EO^2 + 5^2$<BR>\n" );
document.write( "    * $289 = EO^2 + 25$<BR>\n" );
document.write( "    * $EO^2 = 289 - 25 = 264$<BR>\n" );
document.write( "    * $EO = \sqrt{264} = 2\sqrt{66}$<BR>\n" );
document.write( "* **Finding Diagonals:**<BR>\n" );
document.write( "    * FD = 2 * FO = 2 * 5 = 10<BR>\n" );
document.write( "    * AE = 2 * EO = 2 * $2\sqrt{66}$ = $4\sqrt{66}$<BR>\n" );
document.write( "* **Area of Rhombus ADEF:**<BR>\n" );
document.write( "    * Area = (1/2) * (diagonal 1) * (diagonal 2)<BR>\n" );
document.write( "    * Area = (1/2) * 10 * $4\sqrt{66}$<BR>\n" );
document.write( "    * Area = $20\sqrt{66}$\r<BR>\n" );
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document.write( "**2. Finding the area of Parallelogram ABCE**\r<BR>\n" );
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document.write( "* **Properties of a Parallelogram:**<BR>\n" );
document.write( "    * Opposite sides are equal and parallel.<BR>\n" );
document.write( "* **Given:**<BR>\n" );
document.write( "    * CD = 11<BR>\n" );
document.write( "    * EF = 17<BR>\n" );
document.write( "* **Finding AE:**<BR>\n" );
document.write( "    * since ADEF is a rhombus, AE=EF. Therefore AE = 17.<BR>\n" );
document.write( "* **Finding the Height of the Parallelogram:**<BR>\n" );
document.write( "    * The height of the parallelogram is the same as the length EO.<BR>\n" );
document.write( "    * Height = $2\sqrt{66}$<BR>\n" );
document.write( "* **Finding the Area of the Parallelogram:**<BR>\n" );
document.write( "    * Area = base * height<BR>\n" );
document.write( "    * Area = AE * EO<BR>\n" );
document.write( "    * Area = 17 * $2\sqrt{66}$<BR>\n" );
document.write( "    * Area = $34\sqrt{66}$\r<BR>\n" );
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document.write( "**3. Finding the Area of the Composite Figure**\r<BR>\n" );
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document.write( "* **Total Area:**<BR>\n" );
document.write( "    * Area of composite figure = Area of Rhombus ADEF + Area of Parallelogram ABCE<BR>\n" );
document.write( "    * Total Area = $20\sqrt{66} + 34\sqrt{66}$<BR>\n" );
document.write( "    * Total Area = $54\sqrt{66}$\r<BR>\n" );
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document.write( "**Therefore, the area of the composite figure is $54\sqrt{66}$.**<BR>\n" );
document.write( " </SPAN>\n" );
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