One Drag, Two Multipliers
Drag the far corner to scale the rectangle up or down, keeping it exactly the same shape. Watch the side length and the area listed below it change at two very different rates.
Side × 1.5, but area × 2.25
Every side is 1.5 times as long as the original.
- Side ratio
- × 1.5
- Area ratio
- × 2.25
- Original area
- 4.42
- Scaled area
- 9.95
Jump to a scale
Ready to try some? Similar figures worksheets
Where it usually goes wrong
Similar figures are defined by every side scaling by the same factor k, which reads as "everything about the shape scales by k" — so a photo enlarged to twice the width is expected to cover twice the paper, and the real answer, four times as much, feels like a separate fact about area rather than a consequence of the same k appearing twice in a product.
Try this
- Drag the corner out to roughly double the rectangle's size. Read the side ratio and the area ratio in the readout — one of them is not what the other suggests it should be.
- Press "Grow ×2" and then "Grow ×3". The side ratios go 2, 3 — evenly spaced — while the area ratios go 4, 9, spreading apart faster each time.
- Press "Shrink ×0.5". The side is now HALF as long, and the area is a QUARTER — shrinking obeys the same squared relationship as growing does.
Where this goes next
This is why doubling a recipe's linear dimensions (a cake pan twice as wide and twice as deep) needs four times the batter for one layer, and why a scale model's paint coverage, fabric, or material cost almost never scales the way its height does.