document.write( "Question 186035: Question: Given an isosceles triangle with a smaller base 0f 2, a perimeter of 70, and acute base angles of 60 degrees, find the trapezoid's area.\r
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\n" ); document.write( "\n" ); document.write( "Work done so far: I know the formula for Area of trapezoid is $\"%28B%5B1%5D%2BB%5B2%5D%29%28H%2F2%29\"$ .
\n" ); document.write( "b1 is 2 but I don't know if I draw altitudes for the trapezoid, the altitudes will equal 2 because the altitudes will make a square. I'm not sure on that part. \n" ); document.write( "

Algebra.Com's Answer #139556 by Edwin McCravy(20055) $\"\"$ $\"About$

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Given an isosceles trapezoid with a smaller base 0f 2, a perimeter of 70, and acute base angles of 60 degrees, find the trapezoid's area.
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document.write( "Let the slanted sides of the trapezoid be X:\r\n" );
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document.write( "Draw in these two altitudes of the trapezoid, and\r\n" );
document.write( "let their lengths be H:\r\n" );
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document.write( "Now we look at only the right triangle on the \r\n" );
document.write( "left, letting its bottom side's length be Z\r\n" );
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document.write( "Now we know that \r\n" );
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document.write( " and \r\n" );
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document.write( " and  \r\n" );
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document.write( "We also know that  and \r\n" );
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document.write( "so\r\n" );
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document.write( "  and \r\n" );
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document.write( "  and \r\n" );
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document.write( "so we replace  by  and H by \r\n" );
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document.write( "Now we go back to the trapezoid:\r\n" );
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document.write( "We know the small segment on the bottom is 2 because\r\n" );
document.write( "the top side of the trapezoid is 2.  And we know that\r\n" );
document.write( "the right segment on the bottom is also  because\r\n" );
document.write( "the right triangle on the left and the one on the right \r\n" );
document.write( "are congruent.\r\n" );
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document.write( "Now we are told that the perimeter is 70.\r\n" );
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document.write( "So to form the perimeter, we add up all four sides of the \r\n" );
document.write( "trapezoid.\r\n" );
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document.write( "The left side of the trapezoid is \r\n" );
document.write( "The bottom side is this sum \r\n" );
document.write( "The right side is \r\n" );
document.write( "The top side is .\r\n" );
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document.write( "So the sum of all those must equal 70:\r\n" );
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document.write( "We solve that for X and get 22\r\n" );
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document.write( "So now we know that the bottom side is\r\n" );
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document.write( "and that is the larger base of the trapezoid.\r\n" );
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document.write( "And its height is .\r\n" );
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document.write( "Now we can find the area using , , and\r\n" );
document.write( ", in the formula\r\n" );
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document.write( "Edwin

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