Ratio of Areas Unit 11 Section 7 Find the ratio of areas of two triangles. Understand and apply the relationships between scale factors, perimeters, and areas of similar figures.

Ratio of Areas Comparing Areas of Triangles 1.If two triangles have equal heights, then the ratio of their area equals the ratio of their bases. 2.If two triangles have equal bases, then the ratio of their areas equals the ratio of their heights. 3.If two triangles are similar, then the ratio of their areas equals the square of their scale factor. Theorem 11-7 If the scales factor of two similar figures is a:b, then a.The ratio of the perimeters is a:b b.The ratio of the areas is a ² :b ²

Example 1: The table refers to similar figures. Complete the table. 123 Scale Factor3:5 Ratio of Perimeters7:4 Ratio of Areas25:9 Practice: Lesson Notes 11.7 Example 1

Find the ratio of the areas in each figure below Example 2: △ ABC: △ ADB 12 B A D C 6 3 Example 3: △ ABD: △ BCD 6 4 AC D 9 B Practice: Lesson 11.7 Notes Example 2

Closure 1.The ratio of the corresponding heights of tow similar triangles is 3:5. What is the ratio of the corresponding sides? Of the perimeters? Of the areas? Classify each statement as true or false. 2.If two quadrilaterals are similar, then their areas must be in the same ratio as the square of the ratio of their perimeters. 3.If the ratio of the areas of two equilateral triangles is 1:3, then the ratio of the perimeters is 1:. 4.If the ratio of the perimeters of two rectangles is 4:7, then the ratio of their areas must be 16:49 5.If the ratio of the areas of two squares is 3:2, then the ratio of their sides must be. Homework: Practice Worksheet 11.7