Area ratio of similar figures
SAT glossary · Math
Definition
Areas scale as the square of the side ratio, so areas in the ratio 9:25 mean sides in the ratio √(9/25)=3:5. The trap is reporting the area ratio unchanged as the side ratio.
Area ratio of similar figures in plain English
When two shapes are similar (same shape, different size), there's a neat rule connecting how their sides scale to how their areas scale: if the sides are in some ratio, the AREAS are in that ratio SQUARED. So if you're told two similar figures have areas in the ratio 9:25, don't assume the sides are also 9:25 — you have to undo the squaring by taking the square root of each number: √(9)=3 and √(25)=5, so the actual side ratio is 3:5. It makes sense if you think about scaling up a square: if you double every side (ratio 2:1), the area doesn't just double — it quadruples (2^2=4), because area is a two-dimensional measurement.
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