Shaded Stripes

What fraction of this square region is shaded? Stripes are equal in width, and the figure is drawn to scale.

Source: Julia Robinson Mathematics Festival

SOLUTION

Suppose without loss of generality that the width of the stripes equals 1 unit.
Draw a 6\times 6 grid as shown in the above figure.

Area of shaded stripe A equals 11 square units.
Area of shaded stripe B equals 7 square units.
Area of shaded stripe C equals 3 square units.
Total area of shaded stripes A,B,C=11+7+3=21 square units.
Area of square region = 6\times 6=36 square units.
Shaded stripes’ fraction of this square region = \frac{21}{36}=\frac{7}{12}.

Answer: \frac{7}{12}.

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About mvtrinh

Retired high school math teacher.
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