2.6: Perimeters and Areas of Similar Figures

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Presentation transcript:

2.6: Perimeters and Areas of Similar Figures

Perimeters of Similar Figures When two figures are similar: The ratio of their perimeters is equal to the ratio of their corresponding side lengths.

Finding the Ratios of Perimeters Find the ratio (red to blue) of the perimeters of the similar rectangles. The ratio of the perimeters is

Areas of Similar Figures When two figures are similar: The ratio of their areas is equal to the square of the ratio of their corresponding side lengths.

Finding Ratios of Areas Find the ratio (red to blue) of the areas of the similar triangles. The ratio of the areas is

Using Proportions to Find Perimeters and Areas A swimming pool is similar in shape to a volleyball court. Find the perimeter P and the area A of the pool. The rectangular pool and the court are similar. So, use the ratio of corresponding side lengths to write and solve proportions to find the perimeter and area of the pool.

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? Determine the ratio (green to blue) of perimeters of the similar rectangles. EX 6 P = 32 RATIO OF SIDES: 9 P = 48 10 15 RATIO of sides is same as perimeter The ratio of perimeters is 2/3.

Find the ratio (yellow to blue) of the perimeters. You Try it: 3 6 5 10 Find the ratio (yellow to blue) of the perimeters. Ratio of Perimeters Yellow perimeter Blue perimeter 16 32 LEFT COLUMN QUESTION How are ratio of perimeters and ratio of side lengths related 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 BLUE 18 GREEN 8 3 2 4 6 RATIO OF SIDES: RATIO OF AREAS The ratio of sides squared is the ratio of areas Compare the relationship between the two ratios. (They are not the same)

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

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