1. Perimeters and Areas of Similar Figures
Geometry
Perimeters and Areas of Similar Figures

2. Is this statement True or False?
The picture is twice as big as our smaller TV.
Screen Size: 6  9
Screen Size: 12  18
Area: 54
Area: 216
April 27, 2017

3. Goals Compare perimeters and areas of similar figures.
Use perimeters and areas of similar figures to solve problems.
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4. Problem 6 24 Draw a rectangle that measures 3  2. The area is ?
Double the lengths of the sides and draw a rectangle that measures 6  4.
The area is ? 24
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5. Example continued
When the lengths of the sides were doubled, did the area double?
NO! 6 24
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6. ? ? So what happened? 6 24 3 The ratio of the sides: 2
The ratio of the areas: 6 ? 24 4
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7. Notice: 6 24 3 The ratio of the sides: 2 The ratio of the areas: 6 4
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8. Theorem 10.5 The Area of Similar Polygons
If two polygons are similar with lengths of corresponding sides in the ratio a:b, then the ratio of their areas is a2:b2.
Another way of saying it: the ratio of the areas is the square of the ratio of the sides.
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9. Example 1 ABCDE ~ MNOPQ 4 6 O P D C B N E Q A M
Find the ratio of the areas of the figures.
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10. Example 2
These figures are similar. The area of the smaller one is 20. Find the area of the larger figure. 4
Ratio of the sides:
Ratio of their areas: 10
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11. Example 2 continued 20 125 x Write the proportion and solve: 4 10
Ratio of sides 2:5
Ratio of areas 4:25
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12. Your Turn 5
These figures are similar. The area of the larger one is 320. Find the area of the smaller figure. ? 8
320
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13. Solution 5
125 ? 8
320
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14. Now do you see how it works?
Do NOT write
Ratio of sides.
5(320) = 1600 and 8(125)=1000
Instead write
Ratio of SQUARE of sides.
25(320) = 8000 and 64(125) = 8000
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15. Try it again…
These figures are similar. Find the area of the smaller figure if the area of the larger one is 720. 5 12
A = 720
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16. Solution 5 12
A = 720
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17. Problem
If the figures are similar, what is the length of the side marked x? 4
A = 36 x
A = 100
Remember: the ratio of the areas is the square of the ratios of the sides.
Or, the ratio of the sides is the square root of the ratios of the areas.
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18. Problem Solution 4 A = 36 x A = 100
The ratio of the sides is the square root of the ratios of the areas.
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19. Here’s nothing surprising:
If two polygons are similar, the ratio of the perimeters is equal to the ratio of the sides. 4 6 2 3
Perimeter = 10
Perimeter = 20
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20. Example ABCD ~ DEFG. AB = 8 and DE = 12. The perimeter of ABCD is 20.
What is the perimeter of DEFG?
Solution:
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21. Summary
The ratio of the areas of similar figures is the square of the ratio of the sides.
The ratio of the perimeters of similar figures is the same as the ratio of the sides.
The ratio of the sides in two similar figures is the square root of the ratio of the areas.
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22. Do you get it? Do these problems.
1. Figure CAT is similar to BAT.
CA = 10 and BA = 15.
What is the ratio of the sides?
What is the ratio of the perimeters of CAT to BAT?
What is the ratio of the areas of CAT to BAT?
2/3
2/3
4/9
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23. 2. Figure RATS is similar to DOGS. RA = 12 and DO = 30.
What is the ratio of the perimeters of RATS to DOGS?
What is the ratio of the areas of RATS to DOGS?
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24. 3. Two figures, ABCDE and XYZWS are similar
3. Two figures, ABCDE and XYZWS are similar. The perimeter of ABCDE is and the perimeter of XYZWS is 18. What is the ratio of corresponding sides? (What is the scale factor?)
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25. 4. JKL ~ RST. The area of JKL is 25 and the area of RST is 64
4. JKL ~ RST. The area of JKL is 25 and the area of RST is 64. What is the ratio of their perimeters?
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26. Ratio of Areas: Ratio of Perimeters:
5. HOT ~ DOG. The area of HOT is 100 and the area of DOG is 9. The perimeter of HOT is 40. What is the perimeter of DOG?
Ratio of Areas: Ratio of Perimeters:
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27. 4. HOT ~ DOG. The area of HOT is 100 and the area of DOG is 9
4. HOT ~ DOG. The area of HOT is 100 and the area of DOG is 9. The perimeter of HOT is 40. What is the perimeter of DOG?
Ratio of Perimeters:
April 27, 2017