document.write( "Question 1002922: Emily made a sketch of a octagonal window on a 27 in squad piece of paper. First she cut 4 identical isosceles triangles from the corners of the paper. Then she cut a square from the center of the octagon. Each leg of the cut-off triangle is 1/3 the length of the paper. The side length of the cut-out square is also a 1/3 the length of the paper. What is the area of the sketch after she removed the triangles and the square?
\n" ); document.write( "I tried: area of original - area of cut outs
\n" ); document.write( "27*27 - 4(27) + 4(9)+
\n" ); document.write( "729 - 108 + 36=585\r
\n" ); document.write( "\n" ); document.write( "Wrong; the right answer is 486 square inches. How? \n" ); document.write( "
Algebra.Com's Answer #619852 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
You forgot about the fact that the triangles have base = height = 9 (since 9 is 1/3 of 27)\r
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\n" ); document.write( "\n" ); document.write( "Also, the area of the square is not 4*9 it is 9*9\r
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\n" ); document.write( "\n" ); document.write( "Finally, you don't add in the square cutout. You subtract it off.\r
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\n" ); document.write( "\n" ); document.write( "Area of paper = s*s = 27*27 = 729
\n" ); document.write( "Area of triangles = 4*(b*h)/2 = 4*(9*9)/2 = 162
\n" ); document.write( "Area of square cutout = 9*9 = 81\r
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\n" ); document.write( "\n" ); document.write( "Area of sketch = (Area of paper) - (triangles) - (square cutout)
\n" ); document.write( "Area of sketch = (729) - (162) - (81)
\n" ); document.write( "Area of sketch = 486 square inches\r
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