document.write( "Question 1166972: In the diagram, triangle ABC is inscribed with diameter AC. Semicircles are constructed having AB and BC as diameters. The total area represented by regions a and b, in square units, is:
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Algebra.Com's Answer #791561 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "            The description in the post is not clear enough to identify the areas of the interest by a unique way.\r
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\n" ); document.write( "\n" ); document.write( "            I will interpret the post as \" to find the sum of the areas of the two lunes \".\r
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\n" ); document.write( "\n" ); document.write( "            For the meaning of the term \" lune \" in Geometry see this Wikipedia article\r
\n" ); document.write( "\n" ); document.write( "            https://en.wikipedia.org/wiki/Lune_(geometry)\r
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document.write( "The diameter is  d =    (Pythagoras),  or\r\n" );
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document.write( "    d^2 = 20^2 + 21^2 = 841.\r\n" );
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document.write( "The area of the large upper-right semi-circle is therefore  \r\n" );
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document.write( "     =  = .\r\n" );
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document.write( "From it, subtract the area of the right angled triangle with the legs 20 and 21; this area is  = 210.\r\n" );
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document.write( "You will get the sum of areas of two segments of the large circle\r\n" );
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document.write( "    segments_area = .               (1)\r\n" );
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document.write( "The area of two smaller semi-circles is  \r\n" );
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document.write( "     =      (2)\r\n" );
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document.write( "( ! same as the area of the large semi-circle !)\r\n" );
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document.write( "Finally, to find the area under the problem's question, you should subtract the area of two segments  (1)  \r\n" );
document.write( "from the area of two small semicircles   of (2).\r\n" );
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document.write( "You will get then the answer to the problem's question as  210 square units.\r\n" );
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