Warm-up
Three quick questions from earlier lessons.
Discover
A 2 by 3 rectangle is enlarged with scale factor 2. What is the area of the new rectangle?
- 24
- 12
Key idea
Similar figures: a dilation (and rigid moves) apart.
Two figures are similar if a sequence of rigid transformations and dilations maps one onto the other: corresponding angles are equal and corresponding lengths are in the same ratio . Perimeters scale by , areas by (and volumes by ).
Worked example
Similar triangles with scale factor 3; the small one has perimeter 12 and area 6.
Perimeter
Lengths × 3.
Area
Areas × 9.
Your turn, guided
Your turn: scale factor 4, small area 5. The large area.
5 × 16.
Practice ★
- Two polygons are similar. A side of length 5 corresponds to a side of length 15. Another side of the small polygon has length 9. Find the matching side of the large one.
- Two polygons are similar. A side of length 5 corresponds to a side of length 20. Another side of the small polygon has length 4. Find the matching side of the large one.
- A polygon has perimeter 20. It is enlarged by a scale factor of 5. Find the new perimeter.
Watch out!
Practice ★★
- A shape has area 9. It is enlarged by a scale factor of 2. Find the new area.
- A shape has area 22. It is enlarged by a scale factor of 4. Find the new area.
Exit ticket
Three questions to check you have got it.
- Two polygons are similar. A side of length 5 corresponds to a side of length 15. Another side of the small polygon has length 9. Find the matching side of the large one.
- Two polygons are similar. A side of length 5 corresponds to a side of length 20. Another side of the small polygon has length 4. Find the matching side of the large one.
- Two polygons are similar. A side of length 3 corresponds to a side of length 15. Another side of the small polygon has length 8. Find the matching side of the large one.
Summary card
Similar figures
Lengths × , perimeters × , areas × .
Watch out: scale by multiplying, and square for areas.