Integrated Math 2 / Unit 6: Similarity
6.6 Area and Perimeter Ratios
Notes
For similar figures with scale factor $k$ (ratio of sides):
- Perimeters have ratio $k$.
- Areas have ratio $k^2$.
- Volumes have ratio $k^3$.
- Example: scale factor 3 turns an area of 5 into $5 \cdot 9 = 45$.
- To find $k$ from areas, take the square root of the area ratio.
Practice
Two similar triangles have a scale factor of 3. The smaller has area 5. What is the area of the larger?
Areas scale by $k^2 = 9$, so $5 \cdot 9 = 45$.
Two similar polygons have areas 16 and 49. What is the ratio of their sides?
Take the square root of the area ratio: $\displaystyle \sqrt{16} : \sqrt{49} = 4 : 7$.
Two similar rectangles have sides in the ratio $2 : 5$. What is the ratio of their areas?
Area ratio is the square of the side ratio: $2^2 : 5^2 = 4 : 25$.
Ready for more? Take the Unit 6 test.