Similar Parallelograms: Finding Area Ratio from 3:4 Side Ratio

Because area involves two dimensions! If each side scales by 3:4, then both length AND width scale by this ratio. So area scales by $3 \times 3 : 4 \times 4 = 9:16$.

Think of a simple example: if a square has side 2 and another has side 4, their sides are in ratio 2:4 = 1:2. Their areas are 4 and 16, which gives ratio 4:16 = 1:4 = $1^2:2^2$!

Yes! This rule applies to all similar shapes - triangles, circles, parallelograms, etc. If the side ratio is a:b, the area ratio is always $a^2:b^2$.

For similar 3D shapes, volume ratios are the cube of the side ratio! If sides are 3:4, volumes are $3^3:4^3 = 27:64$.

Check that all corresponding sides have the same ratio. Here: 10:7.5 = 4:3 and 2:1.5 = 4:3. Since both ratios equal 4:3, the parallelograms are similar!