SOLUTION: A square of side length S and an equilateral triangle of side length S are placed inside a rectangle of length 2S and width S as shown. What fraction of the area of the rectangle r

Question 1061894: A square of side length S and an equilateral triangle of side length S are placed inside a rectangle of length 2S and width S as shown. What fraction of the area of the rectangle remains uncovered?
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Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
Area of rectangle = 2S * S = 2S^2
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Altitude of the equilateral triangle = square root ( S^2 - S^2/4) = (S/2) * square root(3)
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Area of equilateral triangle = (1/2) * S * (S/2) * square root(3) = (S^2/4) * square root (3)
:
S^2 - (S^2/4) * square root (3) = S^2 (1 - (square root (3) / 4)) = 0.567S^2
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Note we use the area of the square, S^2
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0.567S^2 is area uncovered, then
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ratio of area uncovered to area of rectangle = 0.567S^2 / 2S^2 = 0.2835
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0.28 is the fraction of the rectangle's area that is uncovered
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