Similar Triangles: Finding Area Ratio from Similarity Ratio of 7

Because area is two-dimensional! If each side is 7 times longer, then both length and width are multiplied by 7, so area gets multiplied by $7 \times 7 = 49$.

You still square it! If similarity ratio is $\frac{1}{3}$, then area ratio is $\left(\frac{1}{3}\right)^2 = \frac{1}{9}$.

Yes! The area ratio equals similarity ratio squared for any similar shapes: triangles, rectangles, circles, or irregular polygons.

Think of a simple example: if you double all sides of a square, the area becomes 4 times bigger, not 2 times! $2^2 = 4$.

For similar 3D shapes, volume ratio equals similarity ratio cubed! If similarity ratio is 7, volume ratio would be $7^3 = 343$.