SOLUTION: 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 t

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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?
I tried: area of original - area of cut outs
27*27 - 4(27) + 4(9)+
729 - 108 + 36=585
Wrong; the right answer is 486 square inches. How?
Answer by jim_thompson5910(35256) About Me  (Show Source):
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)

Also, the area of the square is not 4*9 it is 9*9

Finally, you don't add in the square cutout. You subtract it off.

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Area of paper = s*s = 27*27 = 729
Area of triangles = 4*(b*h)/2 = 4*(9*9)/2 = 162
Area of square cutout = 9*9 = 81

Area of sketch = (Area of paper) - (triangles) - (square cutout)
Area of sketch = (729) - (162) - (81)
Area of sketch = 486 square inches