Find the Perimeter and Area: 7 6 10 8

Perimeter and Area of Similar Figures Geometry Unit 11, Day 9 Ms. Reed

Proportions and Similar Triangles We will be investigating perimeters and areas of similar rectangles You will need: Graph Paper Calculator Notes Page

On your graph paper: Starting in the corner, draw a 3 unit by 4 unit rectangle Choose 3 scale factors from 2-10 and create those rectangles so that they start at the same corner of the graph. Fill in I, II, and III on Table 1.

Table 2: Using the information from Table 1 to complete Table 2. How do the ratios compare with the scale factors?

What we discovered: 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 a2:b2

Example 1 3 in 5 in The area of the smaller regular hexagon is 30 in2. Find the area of the larger hexagon. What is the ratio of the corresponding sides? What is the ratio of the areas?

Example 1 3 in 5 in 9 = 30 25 x x = 83.3 in2

Example 2 The similarity ratio of 2 triangles is 3:2. The area of the larger triangle is 36cm2. Find the area of the smaller triangle. What is the ratio of the areas? Set up the proportion:

Example 2 9 = 36 4 x x = 16 cm2

Area to Perimeter: (example 3) The areas of two similar triangles are 50cm2 and 98cm2. What is the ratio of their perimeters? Simplify the ratio then Work Backwards!

Example 3 50 98 REDUCE! 25 49 Find the square root 5 7

Example 4 The areas of two similar rectangles are 2940 ft2 and 135 ft2. Find the ratios to their perimeters. Ratio = 14/3

Homework Work Packet: Perimeter and Area of Similar Figures