Similar figures and areas

When two figures are similar, their corresponding sides are proportional. Think of it like scaling a recipe: if you double all ingredients, you make twice as much food. In technical drawing, when you enlarge a figure by a linear scale factor of 2, each side becomes twice longer. However, the area increases by the square of that factor—so the area becomes 4 times larger, not 2 times!

Consider designing a shop sign in Lagos. If your original design measures 1m by 1m with area 1m², and you enlarge it by scale factor 3, each side becomes 3m. The new area becomes 9m². This is why: new area = original area × (scale factor)². For reduction, the same rule applies. Always remember that sides change linearly, but areas change by the square of the scale factor.