Calculating Perimeter and Area Ratios of Similar Figures
Calculating perimeter and area ratios of similar figures is a Grade 7 geometry skill in Big Ideas Math Advanced 2, Chapter 2: Transformations. For similar figures with scale factor k, the perimeter ratio equals k and the area ratio equals k squared. For example, similar figures with side ratio 3:2 have a perimeter ratio of 3:2 and an area ratio of 9:4.
Key Concepts
For similar figures with scale factor $k$: $$\frac{\text{Perimeter} 1}{\text{Perimeter} 2} = k$$ $$\frac{\text{Area} 1}{\text{Area} 2} = k^2$$.
Common Questions
What is the relationship between scale factor and perimeter for similar figures?
The perimeter ratio equals the scale factor k. If one figure has sides twice as long, its perimeter is also twice as large.
What is the relationship between scale factor and area for similar figures?
The area ratio equals k squared. If scale factor is 3:2, the area ratio is 9:4.
How do you find the area ratio from a perimeter ratio?
Square the perimeter ratio. If the perimeter ratio is 4:7, the area ratio is 16:49.
What textbook covers perimeter and area ratios in Grade 7?
Big Ideas Math Advanced 2, Chapter 2: Transformations covers how scale factors affect perimeter and area in similar figures.