1. Splash Screen

2. Lesson Menu Five-Minute Check (over Lesson 11–4) NGSSS Then/Now Theorem 11.1: Areas of Similar Polygons Example 1: Find Areas of Similar Polygons Example 2: Use Areas of Similar Figures Example 3: Real-World Example: Scale Models

3. Over Lesson 11–4 A.A B.B C.C D.D 5-Minute Check 1 A.48 cm 2 B.144 cm 2 C.166.3 cm 2 D.182.4 cm 2 What is the area of a regular hexagon with side length of 8 centimeters? Round to the nearest tenth if necessary.

4. Over Lesson 11–4 A.A B.B C.C D.D 5-Minute Check 2 A.784 in 2 B.676 in 2 C.400 in 2 D.196 in 2 What is the area of a square with an apothem length of 14 inches? Round to the nearest tenth if necessary.

5. Over Lesson 11–4 A.A B.B C.C D.D 5-Minute Check 3 A.120 units 2 B.114 units 2 C.108 units 2 D.96 units 2 Find the area of the figure. Round to the nearest tenth if necessary.

6. Over Lesson 11–4 A.A B.B C.C D.D 5-Minute Check 4 A.184 units 2 B.158.9 units 2 C.132.6 units 2 D.117.7 units 2 Find the area of the figure. Round to the nearest tenth if necessary.

7. Over Lesson 11–4 A.A B.B C.C D.D 5-Minute Check 5 A.11 units 2 B.12 units 2 C.13 units 2 D.14 units 2 Find the area of the figure.

8. Over Lesson 11–4 A.A B.B C.C D.D 5-Minute Check 6 A.346 m 2 B.299.6 m 2 C.173 m 2 D.149.8 m 2 Find the area of a regular triangle with a side length of 18.6 meters.

9. NGSSS MA.912.G.2.6 Use coordinate geometry to prove properties of congruent, regular and similar polygons, and to perform transformations in the plane. MA.912.G.2.7 Determine how changes in dimensions affect the perimeter and area of common geometric figures.

10. Then/Now You used scale factors and proportions to solve problems involving the perimeters of similar figures. (Lesson 7–2) Find areas of similar figures by using scale factors. Find scale factors or missing measures given the areas of similar figures.

11. Concept

12. Example 1 Find Areas of Similar Polygons If ABCD ~ PQRS and the area of ABCD is 48 square inches, find the area of PQRS. The scale factor between PQRS and ABCD is or. So, the ratio of the areas is __ 9 6 3 2

13. Example 1 Find Areas of Similar Polygons Write a proportion. Multiply each side by 48. Simplify. Answer:So, the area of PQRS is 108 square inches.

14. A.A B.B C.C D.D Example 1 A.180 ft 2 B.270 ft 2 C.360 ft 2 D.420 ft 2 If EFGH ~ LMNO and the area of EFGH is 40 square inches, find the area of LMNO.

15. Example 2 Use Areas of Similar Figures The area of ΔABC is 98 square inches. The area of ΔRTS is 50 square inches. If ΔABC ~ ΔRTS, find the scale factor from ΔABC to ΔRTS and the value of x. Let k be the scale factor between ΔABC and ΔRTS.

16. Example 2 Use Areas of Similar Figures Theorem 11.1 Substitution Take the positive square root of each side. Simplify. So, the scale factor from ΔABC to ΔRTS is Use the scale factor to find the value of x.

17. Example 2 Use Areas of Similar Figures The ratio of corresponding lengths of similar polygons is equal to the scale factor between the polygons. Substitution 7x= 14 ● 5Cross Products Property. 7x= 70Multiply. x= 10Divide each side by 7. Answer:x = 10

18. Example 2 Use Areas of Similar Figures CHECKConfirm that is equal to the scale factor.

19. A.A B.B C.C D.D Example 2 A.3 inches B.4 inches C.6 inches D.12 inches The area of ΔTUV is 72 square inches. The area of ΔNOP is 32 square inches. If ΔTUV ~ ΔNOP, use the scale factor from ΔTUV to ΔNOP to find the value of x.

20. Example 3 Scale Models CRAFTS The area of one side of a skyscraper is 90,000 square feet. The area of one side of a scale model is 200 square inches. If the skyscraper is 720 feet tall, about how tall is the model? UnderstandThe sides of the skyscraper and the scale model are similar. You need to find the scale factor from the skyscraper to the scale model. PlanThe ratio of the areas of the sides of the two figures is equal to the square of the scale factor between them. Before comparing the two areas, write them so that they have the same units.

21. Example 3 Scale Models Solve Convert the areas of the scale model to square feet. Next, write an equation using the ratio of the two areas in square feet. Let k represent the scale factor between the two sides. 1.389 ft 2

22. Example 3 Scale Models Theorem 11.1 Substitution 1.54 ● 10 –5 = k 2 Simplify using a calculator.

23. Example 3 Scale Models Answer:The scale model is about 34 inches tall. So, the model’s height is the height of the skyscraper. Multiply the height of the skyscraper by the scale factor and convert to inches.

24. Example 3 Scale Models CHECKMultiply the area of the side of skyscraper by the square of this scale factor and compare to the given area of the side of the scale model.

25. A.A B.B C.C D.D Example 3 A.4.3 inches B.5.8 inches C.6.7 inches D.7.2 inches MODELS The area of one hood of a car is 35 square feet. The area of the hood of a model is 6 square inches. If the car is 14 feet long, about how long is the model?

26. End of the Lesson