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Perimeters & Areas of Similar Figures

Perimeters & Areas of Similar Figures. Objectives: To find perimeters & areas of similar figures. Reminder of Perimeter & Area. Perimeter – Distance around a figure Perimeter of any polygon - add up the lengths of all of the sides Perimeter of a circle – Circumference C = 2 r

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Perimeters & Areas of Similar Figures

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  1. Perimeters & Areas of Similar Figures Objectives: To find perimeters & areas of similar figures.

  2. Reminder of Perimeter & Area • Perimeter – Distance around a figure • Perimeter of any polygon - add up the lengths of all of the sides • Perimeter of a circle – Circumference • C = 2r • Area – How much 2D space it takes up • A// = bh • AΔ = ½ bh • A = r2

  3. Perimeters & Areas of similar figures • If the similarity (side) ratio of 2 similar figures is a/b, then • The ratio of their perimeters is a/b. • The ratio of their areas is a2/b2. b a

  4. Ex.1 Find the ratio of the perimeter and the Area (Larger to smaller) ΔABC ~ ΔFDE D 5 Side ratio = 4 7.5 5 B E F 6.25 6 Perimeter Ratio = Side Ratio Perimeter Ratio = 5/4 Area Ratio = a2/b2 = 4 A C 5 52/42 = 25/16

  5. Ex.2: Find the area The ratio of the lengths of the corresponding sides of 2 regular octagons is 8/3. The area of the larger octagon is 320ft2. Find the area of the smaller octagon. 8 Side ratio = 3 Now, set up an area proportion using the area ratio! 82 64 Area ratio = = 32 9 Large side Large Area 64 320 = 9 x x = 45ft2 Small side

  6. Ex.3: Find the side ratio The areas of 2 similar pentagons are 32in2 and 72in2. What is their similarity (side) ratio? What is the ratio of their perimeter. Reduce Remember: Side ratio is a/b and area ratio is a2/b2. So if the area ratio is given, you must take the square root of the numerator and the denominator. 32 4 2 = = 3 72 9 Area Ratio Side Ratio and the Perimeter ratio

  7. Ex.4: Find the perimeter & area of similar figures. The similarity (side) ratio of two similar Δis 5:3. The perimeter of the smaller Δ is 36cm, and its area is 18cm2. Find the perimeter & area of the larger Δ. Write the side ratio and then find the perimeter. Write the area ratio and then find the area. 52 25 A 5 P = = = 32 9 18 3 36 PL = 60cm A = 50cm2

  8. What have I Learned?? • Side Ratio = a/b • Perimeter Ratio = a/b • Area Ratio = a2/b2 • If perimeters are given: • Write as a ratio • Reduce to simplest form for the side ratio • If Areas are given: • Write as a ratio • Reduce until 2 perfect squares are reached. • Square Root (√) both numerator & denominator for the side ratio

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