1. Areas of Similar Triangles
LESSON 11–5
Areas of Similar Triangles

2. Five-Minute Check (over Lesson 11–4) TEKS 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
Lesson Menu

3. What is the area of a regular hexagon with side length of 8 centimeters? Round to the nearest tenth if necessary.
A. 48 cm2
B. 144 cm2
C cm2
D cm2
5-Minute Check 1

4. What is the area of a square with an apothem length of 14 inches
What is the area of a square with an apothem length of 14 inches? Round to the nearest tenth if necessary.
A. 784 in2
B. 676 in2
C. 400 in2
D. 196 in2
5-Minute Check 2

5. Find the area of the figure. Round to the nearest tenth if necessary.
A. 120 units2
B. 114 units2
C. 108 units2
D. 96 units2
5-Minute Check 3

6. Find the area of the figure. Round to the nearest tenth if necessary.
A. 184 units2
B units2
C units2
D units2
5-Minute Check 4

7. Find the area of the figure.
A. 11 units2
B. 12 units2
C. 13 units2
D. 14 units2
5-Minute Check 5

8. Find the area of a regular triangle with a side length of 18.6 meters.
A. 346 m2
B m2
C. 173 m2
D m2
5-Minute Check 6

9. Mathematical Processes G.1(A), G.1(F)
Targeted TEKS
G.10(B) Determine and describe how changes in the linear dimensions of a shape affect its perimeter, area, surface area, or volume, including proportional and non-proportional
dimensional change.
Mathematical Processes
G.1(A), G.1(F)
TEKS

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

11. Concept

12. 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
Example 1

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

14. If EFGH ~ LMNO and the area of EFGH is 40 square inches, find the area of LMNO.
A. 180 ft2
B. 270 ft2
C. 360 ft2
D. 420 ft2
Example 1

15. Let k be the scale factor between ΔABC and ΔRTS.
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.
Example 2

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

17. 7x = 14 ● 5 Cross Products Property. 7x = 70 Multiply.
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 ● 5 Cross Products Property.
7x = 70 Multiply.
x = 10 Divide each side by 7.
Answer: x = 10
Example 2

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

19. The area of ΔTUV is 72 square 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.
A. 3 inches
B. 4 inches
C. 6 inches
D. 12 inches
Example 2

20. Answer: The dimensions of the first banner increase
Changing Dimensions
CRAFTS Jonathon has a banner that measures 15 feet by 6 feet. He makes two additional banners that measure 30 feet by 12 feet and 30 feet by 10 feet, respectively. Describe how the difference in dimensions affects the areas of the banners.
Answer: The dimensions of the first banner increase
proportionally by a scale factor of 2, so the area of
the first banner is 4 times the area of the original
banner. On the second banner, the width doubles
and the length increases by about 1.67 so it is a
non-proportional change. The area of the second
banner increases by the product of the scale
factors of each dimension, so the area is 3.34 times
greater than the area of the original.
Example 3

21. MODELS The area of one hood of a car is 35 square feet
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?
A. 4.3 inches
B. 5.8 inches
C. 6.7 inches
D. 7.2 inches
Example 3

22. Areas of Similar Triangles
LESSON 11–5
Areas of Similar Triangles