10.4 Perimeters & Areas of Similar Figures

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Presentation transcript:

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

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

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

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

Complete the Chart: Rectangle Perimeter Area Original 1 2 3

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

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

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

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.

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.

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

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.

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?

Homework P. 555 2-8 even, 9, 12-20 even, 26-30 even