document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209964>Question 1209964</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ACDF is a Parallelogram. DEF is a sector. ABC is a right triangle. Solve for the area of the composite figure.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #851261 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=851261\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Okay, let's break down this problem step-by-step.\r<BR>\n" );
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document.write( "**1. Area of the Right Triangle ABC:**\r<BR>\n" );
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document.write( "* Since ABC is a right triangle with AB = 4 cm and BC = 4 cm, we can use the formula for the area of a triangle:<BR>\n" );
document.write( "    * Area = (1/2) * base * height<BR>\n" );
document.write( "    * Area(ABC) = (1/2) * 4 cm * 4 cm = 8 cm²\r<BR>\n" );
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document.write( "**2. Area of the Parallelogram ACDF:**\r<BR>\n" );
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document.write( "* We know that AF = 20 cm.<BR>\n" );
document.write( "* Since ACDF is a parallelogram, CD = AF = 20 cm.<BR>\n" );
document.write( "* To find the area of the parallelogram, we need the base and the height.<BR>\n" );
document.write( "* Since the height of the parrallelogram is the same as the length of AB and BC, the height is 4cm.<BR>\n" );
document.write( "* Area(ACDF) = base * height<BR>\n" );
document.write( "    * Area(ACDF) = 20 cm * 4 cm = 80 cm²\r<BR>\n" );
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document.write( "**3. Area of the Sector DEF:**\r<BR>\n" );
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document.write( "* We are given that angle EDF = 35 degrees.<BR>\n" );
document.write( "* We need to find the radius of the sector. Since ACDF is a parallelogram, CD = AF. Also, since ABC is a right triangle with AB = BC, then the length of AC = sqrt(4^2 + 4^2) = sqrt(16+16) = sqrt(32) = 4 * sqrt(2). Because ACDF is a parallelogram, then DE = AC = 4 * sqrt(2) cm. This is the radius of the sector.<BR>\n" );
document.write( "* The area of a sector is given by:<BR>\n" );
document.write( "    * Area = (θ/360°) * π * r²<BR>\n" );
document.write( "    * Area(DEF) = (35°/360°) * π * (4√2 cm)²<BR>\n" );
document.write( "    * Area(DEF) = (35/360) * π * 32 cm²<BR>\n" );
document.write( "    * Area(DEF) = (7/72) * 32π cm²<BR>\n" );
document.write( "    * Area(DEF) = (224/72)π cm²<BR>\n" );
document.write( "    * Area(DEF) = (28/9)π cm²<BR>\n" );
document.write( "    * Area(DEF) ≈ 9.77π cm²<BR>\n" );
document.write( "    * Area(DEF) ≈ 30.7 cm²\r<BR>\n" );
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document.write( "**4. Total Area of the Composite Figure:**\r<BR>\n" );
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document.write( "* Total Area = Area(ABC) + Area(ACDF) + Area(DEF)<BR>\n" );
document.write( "* Total Area = 8 cm² + 80 cm² + (28/9)π cm²<BR>\n" );
document.write( "* Total Area = 88 cm² + (28/9)π cm²<BR>\n" );
document.write( "* Total Area ≈ 88 cm² + 30.7 cm²<BR>\n" );
document.write( "* Total Area ≈ 118.7 cm²\r<BR>\n" );
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document.write( "**Therefore, the total area of the composite figure is approximately 118.7 cm².**<BR>\n" );
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