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Upper primary school mathematics question UPQ140

ABCD is a rectangle where AM = MB and AN = ND. What fraction of the rectangle is shaded?

Solution:

Added two lines as the green dotted lines in the rectangle as shown and view it as two rectangles top and bottom.

We can flip the small shaded triangle to fit in the small unshaded triangle in the bottom rectangle.

Fraction of shaded figure in top rectangle = ¼

Fraction of shaded figure in bottom rectangle = ½

Fraction of shaded figure in the rectangle = ¼ + ½ =3/8

Alternative solution:

By flipping the two shaded triangles as the arrows shown in the figure

The fraction of the shaded portion in the rectangle = 1/8 + ¼ = 3/8

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