document.write( "Question 1018212: A quadrilateral contains an inscribed circle. The ratio of the perimeter of the quadrilateral to that of the circle is 4:3. Find the ratio of the area of the quadrilateral to that of the circle. \n" ); document.write( "

Algebra.Com's Answer #634372 by ikleyn(52879) $\"\"$ $\"About$

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\n" ); document.write( "A quadrilateral contains an inscribed circle. The ratio of the perimeter of the quadrilateral to that of the circle is 4:3.
\n" ); document.write( "Find the ratio of the area of the quadrilateral to that of the circle.
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document.write( "If a quadrilateral has/contains an inscribed circle, then the area of the quadrilateral is \r\n" );
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document.write( " = ,\r\n" );
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document.write( "where P is the quadrilateral's perimeter, and r is the radius of the inscribed circle.\r\n" );
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document.write( "It is well known fact. See the lesson Area of a quadrilateral circumscribed about a circle in this site. \r\n" );
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document.write( "From the other side, the circumference of the circle is  = , and the area of the circle S is  = .\r\n" );
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document.write( "Therefore,\r\n" );
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document.write( " =  :  = .\r\n" );
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document.write( "Now recall that   = ,  it is given.\r\n" );
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document.write( "Hence,   = .\r\n" );
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document.write( "The solution is complete.\r\n" );
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