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Section 8 – 6 Perimeters & Areas of Similar Figures

Section 8 – 6 Perimeters & Areas of Similar Figures . Objective: To find the perimeters and areas of similar figures. Theorem 8 – 6 Perimeters & Areas of Similar Figures. If the similarity ratio of two similar figures is , then: 1) The ratio of their perimeter is

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Section 8 – 6 Perimeters & Areas of Similar Figures

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  1. Section 8 – 6Perimeters & Areasof Similar Figures Objective: To find the perimeters and areas of similar figures

  2. Theorem 8 – 6Perimeters & Areas of Similar Figures If the similarity ratio of two similar figures is , then: 1) The ratio of their perimeter is 2) The ratio of their areas is

  3. Example 1 Finding Ratios in Similar Figures • The trapezoids at the right are similar. The ratio of the lengths of corresponding sides is , or . • Find the ratio of the smaller trapezoids perimeter to the larger trapezoids perimeter. • In the same order as above, find the ratio of the areas.

  4. B) Two similar polygons have corresponding sides in the ratio 5:7. • Find the ratio of their perimeters. • Find the ratio of their areas.

  5. C) The triangles below are similar. Find the ratio (larger to smaller) of their perimeters and of their areas. • Find the ratio of their perimeters. • Find the ratio of their areas.

  6. Example 2 Finding Areas Using Similar Figures A) The area of the smaller regular polygon is about 27.5 . Find the area of the larger regular pentagon.

  7. B) The corresponding sides of two similar parallelograms are in the ratio 3:4. The area of the larger parallelogram is 96 . Find the area of the smaller parallelogram

  8. C) The ratio of the lengths of the corresponding sides of two regular octagons is 8:3. The area of the larger octagon is 320 . Find the area of the smaller octagon.

  9. Example 3 Real-World Connection A) The similarity ratio of the dimensions of two similar pieces of window glass is 3:5. The smaller piece costs $2.50. What should be the cost of the larger piece?

  10. B) Jack plants the same crop in two rectangular fields, each with side lengths in a ratio of 2 : 3. Each dimension of the larger field is 3.5 times the dimension of the smaller field. Seeding the smaller field costs $8. How much money does seeding the larger field cost?

  11. Example 4 Finding Similarity& Perimeter Ratios A) The areas of two similar triangles are 50 and 98 . What is the similarity ratio? What is the ratio of their perimeters?

  12. B) The areas of two similar rectangles are 1875 and 135 . What is the ratio of their perimeters?

  13. C) The areas of two similar pentagons are 32 and7. What is the ratio of their perimeters?

  14. Homework:

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