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Ratios of Areas

Pg 465 HW: pg 458 – 459 1 - 21. Ratios of Areas . 11-7 PG 456. Comparing Areas of Triangles. (Purple Text) Comparing Areas of Triangles 1) If two triangles have equal heights, then the ratio of their areas equals the ratio of their bases.

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Ratios of Areas

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  1. Pg 465 HW: pg 458 – 459 1 - 21 Ratios of Areas 11-7 PG 456

  2. Comparing Areas of Triangles • (Purple Text) • Comparing Areas of Triangles • 1) If two triangles have equal heights, then the ratio of their areas equals the ratio of their bases. • 2) If two triangles have equal bases, then the ratio of their areas equals the ratio of their heights. • 3) If two triangles are similar then the ratio of their areas equals the square of their scale factor.

  3. Example 1) Look in your book, copy down if needed. • A) with equal height • B) With equal bases C) scale factor

  4. 2 examples on the side board& more • Directions: Find the ratio of the areas in each figure below. • 3) The ratio of the corresponding heights of two similar triangles is 3:5. What is the ratio of the corresponding sides? • What is the ratio of the perimeters? • What is the ratio of the areas?

  5. True of False • 4) If two quadrilaterals are similar, then their areas must be in the same ratio as the square of the ratio of their perimeters. • 5) If the ratio of the areas of two equilateral triangles is 1:3, then the ratio of the perimeters is 1: (3)^.5 or the square root of 3. • 6) If the ratio of the perimeters of two rectangles is 4:7, then the ratio of their areas must be 16:49. • 7) If the ratio of the areas of two squares is 3:2 then the ratio of their sides must be (3)^.5 : (2)^.5, square root of both numbers.

  6. Classroom Exercises pg 458, 1 - 15

  7. Answers: 1) 9/5 ; 2) 9/16 ; 3) 5/6 4) 1:3; 1:9 ; 5) 1:5 ; 1:25 6) 3:4 ; 9:16 7) 2:3 ; 4:9 8) 4:5 ; 16:25 9) 3:5 ; 9:25 10) 4:7 ; 4:7 11) 6:5 ; 6:5 12) A) yes B) 3:4 ; 9:16 13) a) No B) tri ABC ~ tri ABC C) 4:25 D) 4:21 14) 8:5 ; 8:15 15) 7:4 ; 49:16

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