Similar figuresSides to 12
Name: Date:
Each pair of shapes is the same shape at two sizes. Find the missing length.
1 cm
2 cm
3 cm
4 cm
5 cm
6 cm
7 cm
8 cm
- Free
- Grade 7
- Whole-number scale factors
Similar figures worksheets
Two shapes are similar when one is a scaled copy of the other: same angles, sides all multiplied by the same number. These free printable worksheets give both figures with one side missing, and finding the scale factor first is what makes the rest easy.
Kid stuck on one? You don’t just get the sheet.
- Answer key included
- Reopen this exact sheet
- Letter & A4 ready
Ready to printSimilar figures
The answer key prints on a separate page.
What's on this sheet
The whole method is two steps. Find a pair of sides that correspond and divide to get the scale factor — 18 against 9 is a factor of 2 — then apply it to the side you want. A child who does it in that order never has to set up a proportion at all, and the arithmetic stays inside the times tables.
Why this sheet works
Which sides correspond is the part that goes wrong. Shapes are drawn in the same orientation here so the pairing is readable, but it is still worth saying out loud: the long side matches the long side. Once figures start being rotated, a child who has been checking the pairing has something to fall back on.
How this one works
One question from this sheet, worked through a step at a time.
Similar figures: 9 and 18
small 9→large 18
18÷9=2
7×2=14
14 cm
- Two shapes, the same shape at two sizes. Every side of the big one is the matching side of the small one multiplied by the SAME number — so the first job is to pair the sides up: long with long, short with short.
- Use the pair you can see both of. 9 became 18, and 18 ÷ 9 = 2 — so every side is 2 times bigger.
- Now the missing side is on the BIG shape, so it grows: 7 × 2 = 14.
- Check it against the picture: the answer should be bigger than 7, and 14 is. So the missing side is 14 cm.