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Ratios of Areas and Perimeters: Triangle, Quadrilateral, Square, and Rectangle

This article explores the ratios of areas and perimeters in various geometric shapes, including triangles, quadrilaterals, squares, and rectangles. Learn how height, base, scale factor, and side lengths affect the relationships between their areas and perimeters.

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Ratios of Areas and Perimeters: Triangle, Quadrilateral, Square, and Rectangle

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  1. Section 11-7 Ratios of Areas

  2. B 3 C A D 6 8 Comparing areas of triangles • If two triangles have equal heights, then the ratio of their areas equals the ratio of their bases.

  3. B D 9 3 A C 15 • If two triangles have equal bases, then the ratio of their areas equals the ratio of their heights.

  4. E B 5 8 A C D F • If two triangles are similar, then the ratio of their areas equals the square of their scale factor.

  5. THEOREM 11-7 • 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

  6. True or False. • If two quadrilaterals are similar, then their areas must be in the same ratio as the square of the ratio of their perimeters. True • If the ratio of the areas of two equilateral triangles is 1:3, then the ratio of the perimeters is 1:3. True

  7. If the ratio of the areas of two squares is 3:2, then the ratio of their sides must be • If the ratio of the perimeters of two rectangles is 4:7, then the ratio of their areas must be 16:49. False True

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