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Ratios of Area of 2D Shapes

Ratios of Area of 2D Shapes. Geometry . Objective. Find the ratio of the area and perimeters of similar shapes while applying the relationships between scale factors, perimeters, and areas of those shapes. What is a Ratio??. A ratio is the comparison of two objects.

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Ratios of Area of 2D Shapes

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  1. Ratios of Area of 2D Shapes Geometry

  2. Objective • Find the ratio of the area and perimeters of similar shapes while applying the relationships between scale factors, perimeters, and areas of those shapes

  3. What is a Ratio?? • A ratio is the comparison of two objects. • A Scale Factor is the ratio of any two corresponding lengths in two similar geometric figures.

  4. Example 8 ft 5 ft Width of Car Length of Car 5 feet = = 1 : 1 ??? 5 in = 8 in Width of model Length of model 5 inches

  5. Ratios of Triangles If two triangles have equal heights, then the ratio of their areas equal the ratio of their bases Height Ratio of Areas = Ratio of Bases Area of Triangle A 8 = Area of Triangle B 3 A B Scale Factor 8 3

  6. Titanic Example • MODEL BUILDING. A scale model of the Titanic is 107.5 inches long and 11.25 inches wide. The Titanic itself was 882.75 feet long. How wide was it? Width of Titanic Length of Titanic = Width of model Length of model LABELS: Width of Titanic = x Width of model ship = 11.25 in Length of Titanic = 882.75 feet Length of model ship = 107.5 in.

  7. Reasoning: Width of Titanic Length of Titanic = Width of model Length of model X feet 882.75 feet = 11.25 in. 107.5 in. 11.25 in.(882.75 feet) x = 107.5 in. x ≈ 92.4 feet

  8. Ratios of Triangles • If two triangles have equal bases, then the ratio of their areas equals the ratio of their heights Area of Triangle A 9 = 9 5 A Area of Triangle B 5 B Scale Factor

  9. Ratios of Triangles • If two triangles are similar, then the ratio of their areas equals the square of their scale factor 3 ( ) 2 Area of Triangle A = 6 Area of Triangle B 6 A 1 4 B = 3

  10. Scale Factor of Similar Figures If the scale factor of two similar figures is a:b. then • The ratio of the perimeters is a:b • The ratio of the areas is a :b 2:1 4:1 2 2 A 2 1 B

  11. Scale Factor Example Find the area and perimeter of two similar figures with a scale factor of 3:5. a:b = 3:5 Ratio of perimeters = a:b = 3:5 Ratio of area = a :b = 9:25 3 5 2 2

  12. Scale Factor Example The ratio of the areas of two similar figures is 1:4. Find the ratio of their perimeters. Ratio of area = Area :Area = 1:4 so a:b = 1:2 Ratio of perimeters =a:b 1:2 Area = 1 a a b Area = 4 b

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