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Ratio of Areas

Ratio of Areas. Wednesday 1/7/09 Section 11-7. What effect does changing a dimension have on the area of a figure?. A. B. h = 6. h = 4. b = 8. b = 8. Comparing Areas of Triangles. If 2 triangles have the equal bases, then the ratio of their areas equals the ratio of their heights. A.

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Ratio of Areas

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  1. Ratio of Areas Wednesday 1/7/09 Section 11-7

  2. What effect does changing a dimension have on the area of a figure? A B h = 6 h = 4 b = 8 b = 8

  3. Comparing Areas of Triangles • If 2 triangles have the equal bases, then the ratio of their areas equals the ratio of their heights. A A= ½ ·8·4 = 16 A= ½ ·8·6 = 24 B h = 6 h = 4 b = 8 b = 8 • Ratio of heights = 6:4 = • Ratio of Areas = 24:16 =

  4. What effect does changing 2 dimensions have on the area of a figure? Both dimensions are doubled. Is the area doubled? B A= ½ ·8·6 = 24 A A= ½ ·4·3 = 6 h = 6 h = 3 b = 8 b = 4

  5. The triangles are similar. If two triangles are similar, then the ratio of their areas equals the square of the scale factor. B A= ½ ·8·6 = 24 A A= ½ ·4·3 = 6 h = 6 h = 3 • Scale Factor = 1:2 • Ratio of Areas = 6:24 = b = 8 b = 4

  6. Comparing Circumferences and Areas of Circles • How does changing the radius effect the ratio of the circumferences? The areas? r= 6 r= 2 C = A= C = A=

  7. Theorem 11-7 • If the scale factor of 2 similar figures is a:b, then the ratio of the perimeters is a:b the ratio of the areas is a2:b2

  8. Geometric Probability Probability = Quantity Desired Total Geometric Probability can be: a) the probability a point is on a portion of a line OR b) the probability a point is in a region

  9. Geometric Probability the probability a point is on a portion of a line If a point P on line segment AB , is picked at random, then the probability it will be on segment AC is C B A Probability = Length of AC Length of AB 0 5 10

  10. Geometric Probability the probability a point is in a region If a point P that lies in rectangle ABCD is picked at random, then the probability it is in region b 2 4 6 A B Probability = Desired Region Total Region 6 a b c D C

  11. Modified Homework Assignment p. 458 1-12, 16, 20 (Wed on HW calendar) p. 463 2,3,5,8 (Today on HW calendar) p. 465 1-10 (Today on HW calendar) TEST is MONDAY

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