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11.7: Ratios of areas

11.7: Ratios of areas. Similar-Figures Theorem. If two figures are similar, then the ratio of their areas equals the square of the ratio of corresponding segments. A 1 , A 2 are the areas of similar figures s 1 , s 2 are the sides of similar figures

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11.7: Ratios of areas

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  1. 11.7: Ratios of areas

  2. Similar-Figures Theorem • If two figures are similar, then the ratio of their areas equals the square of the ratio of corresponding segments. • A1 , A2 are the areas of similar figures • s1 , s2 are the sides of similar figures • The similar figures theorem can only be used when you have similar figures.

  3. Example 1 • Find the ratio of the areas of the polygons. 3 4

  4. Example 2 • Find the ratio of the areas of the polygons. 6 3 8

  5. Example 3 • Find the ratio of the areas of the polygons. 4 9

  6. Example 4 • Find the ratio of the areas of the polygons. 6 6 9 9

  7. Median Area Theorem • The median of any triangle divides it into two triangles with equal areas. B A△ABD = A△CBD Note: The triangles are most often not congruent! C A D

  8. Example 5 • Find the ratio of the areas of… Q a. △PQS : △RQS b. △PQS : △PQR S R P

  9. Example 6 • Find the area of the shaded region to the whole triangle. 4 5

  10. Example 7 • Find the area of the shaded region to the whole triangle. 6 1

  11. Example 8 • Find the ratio of the sides of two regular hexagons whose areas are in the ratio of 24:96.

  12. Homework p. 546 1-6, 10-12, 15

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