9th grade · Math · Unit 6 of 18
Similarity & Scale
Scale factors and similar figures
What your child practices
Using scale factors to find missing sides, solving shadow and scale-drawing problems, and seeing how enlarging a shape changes its area and volume.
Alabama Course of Study content standard: GDA.19; GDA.27; GDA.28 · dilations, scale factors and similar triangles
How we explain it
Children can open this short lesson before they practice.
- Similar shapes have the same shape but different sizes.
- The scale factor is new length ÷ old length.
- Multiply every length by the scale factor. Areas change by the factor squared.
Example: A rectangle 4 cm by 6 cm is enlarged by a scale factor of 3. What are the new sides? 4 × 3 = 12. 6 × 3 = 18. Answer: 12 cm by 18 cm
Similarity & Scale in Alabama
In the Alabama Course of Study, this is unit 6 of 18 in 9th grade Math, after Coordinate Geometry and before Right Triangles & Scaling.
Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.
Sample questions
A taste of this unit. In the app, questions change every time and get easier or harder to match your child.
Question 1
Triangle B is an enlargement of triangle A. A side of 8 cm on triangle A matches a side of 32 cm on triangle B. What is the scale factor?
answer box
4
Hint: Scale factor = new length ÷ original length = 32 ÷ 8 = 4.
Question 2
Two rectangles are similar. The small one is 9 cm by 7 cm. The large one is 45 cm long. How wide is the large rectangle?
answer boxcm
35 cm
Hint: The scale factor is 45 ÷ 9 = 5. Multiply the width by 5: 7 × 5 = 35 cm.
Question 3
△ABC ~ △DEF. AB = 6 cm, BC = 8 cm and DE = 18 cm. How long is EF?
answer boxcm
24 cm
Hint: The sides are in proportion: DE/AB = EF/BC, so EF = 8 × (18/6) = 8 × 3 = 24 cm.
Question 4
A 1 m stick casts a 4 m shadow. At the same time, a tree casts a 24 m shadow. How tall is the tree?
answer boxm
6 m
Hint: The triangles are similar, so height ÷ shadow stays the same: tree = 1 × 6 = 6 m.
Question 5
A scale drawing uses 1 cm for every 20 cm in real life. A wall measures 14 cm on the drawing. How long is the real wall in centimeters?
answer boxcm
280 cm
Hint: Multiply by the scale: 14 × 20 = 280 cm.
Question 6
A cube is enlarged by a scale factor of 2. By what factor does its volume grow?
answer box
8
Hint: Volume uses three lengths, so it grows by 2³ = 8.