1. 10.4 Perimeters & Areas of Similar Figures
Chapter 10: Area
10.4
Perimeters & Areas of Similar Figures

2. Quick Review
Find the perimeter of a rectangle with base 1 cm and height 3 cm.

3. Quick Review
Find the perimeter of a right triangle with height 6 cm and base 8 cm.

4. Group Activity With your partner: Draw a 3 unit by 4 unit rectangle
Draw 3 different rectangles, each similar to the original rectangle, labeled 1, 2, 3

5. Complete the Chart:
Rectangle
Perimeter
Area
Original 1 2 3

6. Complete the Chart Rectangle Similarity Ratio Ratio of Perimeters
Ratio of Areas
1 to original
2 to original
3 to original

7. Question
How do the ratios of perimeters and the ratios of areas compare with the similarity ratios?

8. Theorem 10-7 Perimeters & Areas of Similar Figures
If the similarity ratio of two similar figures is a/b, then:
The ratio of their perimeters is a/b
The ratio of their areas is

9. Example 1
Two trapezoids are similar. The ratio of the lengths of their corresponding sides is 2/3.
Find the ratio (smaller to larger) of the perimeters.
Find the ratio (smaller to larger) of the areas.

10. Example 1a
Two similar polygons have corresponding sides in the ratio 5:7.
Find the ratio of their perimeters.
Find the ratio of their areas.

11. Example 2
The area of the smaller regular pentagon is about 27.5 cm2. What is the best approximation for the area of the larger regular pentagon?
4 cm
10 cm

12. Example 2a
The corresponding sides of two similar parallelograms are in the ratio 3:4. The area of the larger parallelogram is 96 sq. in. Find the area of the smaller parallelogram.

13. Example 4
The areas of two similar triangles are 50 sq. cm. and 98 sq. cm. What is the similarity ratio? What is the ratio of their perimeters?

14. Homework
P. 555
2-8 even, 9, even, even