If two polygons are similar (i.e. corresponding sides are proportional and corresponding angles are equal), then the ratio of the areas of the two polygons is equal to the square of the ratio of a pair of corresponding sides. For example, consider the two similar isosceles triangles, ΔABC and ΔPQR (Figure 1). Area of ΔPQR \( = \frac{1}{2} \cdot 18 \cdot 12 = 108\;{\rm{unit}}{{\rm{s}}^2}\), and area of ΔABC \( = \frac{1}{2} \cdot 6 \cdot 4 = 12\;{\rm{unit}}{{\rm{s}}^2}\). Ratio of areas \( = \frac{{108}}{{12}} = 9\); and square of ratio of corresponding...