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: $\frac{7}{12}$.