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

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

4. Ex.1 Find the ratio of the perimeter and the Area (Larger to smaller) ► ΔABC ~ ΔFDE A B C D E F 4 6 5 6.255 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

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 320ft 2. Find the area of the smaller octagon. Side ratio = 8 3 Area ratio = 8282 3232 = 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

6. 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

7. 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. 5252 3232 = 25 9 = A 18 A = 50cm 2

8. 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