# PH_Geo_10-4_Perimeters_and_Areas_of_Similar_Figures

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### Section 10–4 Perimeters & Areas of Similar Figures:

Section 10–4 Perimeters & Areas of Similar Figures Objectives: 1) To find perimeters & areas of similar figures.

### Reminder of Perimeter & Area:

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 A Δ = ½ bh A = r 2

### Thm(8 – 6) Perimeters & Areas of similar figures:

Thm(8 – 6) 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 a 2 /b 2 . a b

### Ex.1 Find the ratio of the perimeter and the Area (Larger to smaller):

Ex.1 Find the ratio of the perimeter and the Area (Larger to smaller) Δ ABC ~ Δ FDE A B C D E F 4 6 5 6.25 5 7.5 Side ratio = 5 4 Perimeter Ratio = Side Ratio Perimeter Ratio = 5/4 Area Ratio = a 2 /b 2 = 5 2 /4 2 = 25/16

### Ex.2: Find the area:

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 320ft 2 . Find the area of the smaller octagon. Side ratio = 8 3 Area ratio = 8 2 3 2 = 64 9 Now, set up an area proportion using the area ratio! 64 9 = 320 x Large side Small side Large Area x = 45ft 2

### Ex.3: Find the side ratio:

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

### Ex.4: Find the perimeter & area of similar figures.:

Ex.4: Find the perimeter & area of similar figures. The similarity (side) ratio of two similar Δ is 5:3. The perimeter of the smaller Δ is 36cm, and its area is 18cm 2 . Find the perimeter & area of the larger Δ . Write the side ratio and then find the perimeter . 5 3 = P 36 P L = 60cm Write the area ratio and then find the area . 5 2 3 2 = 25 9 = A 18 A = 50cm 2

### What have I Learned??:

What have I Learned?? Side Ratio = a/b Perimeter Ratio = a/b Area Ratio = a 2 /b 2 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