Warm-up
Three quick questions from earlier lessons.
Discover
A 1 cm by 1 cm square is copied with scale factor 3. What is the area of the copy?
- 9 cm²
- 3 cm²
Set k = 3. How many times larger is the area?
- 9 times
- 3 times
Key idea
Lengths scale by , areas by .
In a scaled copy with scale factor , every length is multiplied by , angles stay the same, and every area is multiplied by . For a real area from a scale drawing, scale the lengths first, then multiply.
Worked example
A 4 cm² triangle, scale factor 5.
Area
k² = 25.
cm²
4 · 25.
Your turn, guided
Your turn: area 6 cm², scale factor 2. The copy's area.
6 · 4.
Practice ★
- A figure has an area of 10 cm². A scaled copy uses a scale factor of 6. What is the area of the copy (cm²)?
- A figure has an area of 5 cm². A scaled copy uses a scale factor of 2. What is the area of the copy (cm²)?
- A figure of area 10 cm² has a scaled copy of area 90 cm². What is the scale factor?
Watch out!
Practice ★★
- On a plan with scale 1 cm to 4 m, a room is 4 cm by 7 cm. What is the room's real area (m²)?
- On a plan with scale 1 cm to 4 m, a room is 6 cm by 4 cm. What is the room's real area (m²)?
- Boss problem. On a map with scale 1 cm to 60 m, a rectangular park is 2 cm by 12 cm.
Exit ticket
Three questions to check you have got it.
- A figure has an area of 10 cm². A scaled copy uses a scale factor of 6. What is the area of the copy (cm²)?
- A figure has an area of 5 cm². A scaled copy uses a scale factor of 2. What is the area of the copy (cm²)?
- A figure has an area of 17 cm². A scaled copy uses a scale factor of 4. What is the area of the copy (cm²)?
Summary card
Scaling and area
Lengths × , areas × .
Watch out: scale both sides before multiplying.