IMC 2015 Q13

Three vertical lines have been added to the diagram. These divide the original diagram into 4 rectangles. In each of these, a diagonal divides the rectangle into two triangles of equal area, one shaded and one unshaded. So the total shaded area in the original rectangle is equal to the total unshaded area and is therefore equal to half the area of the original rectangle. So the total shaded area is \(\tfrac{1}{2} \times 3 \times 14\) cm² = 21 cm².