The
fraction of the rectangle that is shaded is equal to the ratio of the area of triangle and the are of
rectangle. First, we need to determine the value of x to be able to calculate
the respective areas. We do as follows:
From the triangle,
tan 45 = 2 / (x/2)
1 = 4 / x
x = 4
L = 4 + 2 = 6
W = 4
A(triangle) = hb / 2 = 2(4) / 2 = 4
A(rectangle) = LW = 6(4) = 24
Fraction shaded = 4 /
24 = 1/6
