Lesson 2. 6: Perimeters and Areas of similar Figures Essential Question: How do changes in side length of similar figures affect the perimeters and areas of the figures? EX RATIO OF SIDES: Determine the ratio (green to blue) of perimeters of the similar rectangles. 6 P = 32 9 P = 48 10 15 The ratio of perimeters is 2/3. RATIO of sides is same as perimeter

You Try it: 3 6 5 Find the ratio (yellow to blue) of the perimeters. 10 Yellow perimeter 16 Ratio of Perimeters Blue perimeter 32 LEFT COLUMN How are ratio of perimeters and ratio of side lengths related QUESTION on similar figures? Answer: Ratios of perimeters is the SAME as ratio of sides of similar figures.

Area of similar figures Determine the ratio of sides and areas (blue to green) of the following figures AREAS 3 2 4 6 RATIO OF SIDES: BLUE 18 GREEN 8 RATIO OF AREAS Compare the relationship between the two ratios. (They are not the same) The ratio of sides squared is the ratio of areas

YOU TRY IT: Find the ratio of the areas of the two similar figures (Red to Blue). 3 AREAS 5 6 10 RATIO OF SIDES LEFT COLLUMN QUESTION: RATIO OF AREAS RED 9 Blue 25 How are the ratio of sides compared to the ratio of areas? Answer: When figures are similar, the ratio of areas is the square of the ratio of sides.

The two figures are similar. Find the ratios (shaded to nonshaded) of the perimeters and of the areas. Ratio of Perimeters: Ratio of Areas: