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

Over Lesson 11–4

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 48 cm2

B. 144 cm2

C. 166.3 cm2

D. 182.4 cm2

What is the area of a regular hexagon with side length of 8 centimeters? Round to the nearest tenth if necessary.

Over Lesson 11–4

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 784 in2

B. 676 in2

C. 400 in2

D. 196 in2

What is the area of a square with an apothem length of 14 inches? Round to the nearest tenth if necessary.

Over Lesson 11–4

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 120 units2

B. 114 units2

C. 108 units2

D. 96 units2

Find the area of the figure. Round to the nearest tenth if necessary.

Over Lesson 11–4

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 184 units2

B. 158.9 units2

C. 132.6 units2

D. 117.7 units2

Find the area of the figure. Round to the nearest tenth if necessary.

Over Lesson 11–4

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 11 units2

B. 12 units2

C. 13 units2

D. 14 units2

Find the area of the figure.

Over Lesson 11–4

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 346 m2

B. 299.6 m2

C. 173 m2

D. 149.8 m2

Find the area of a regular triangle with a side length of 18.6 meters.

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.

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.

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 __96

__32

Find Areas of Similar Polygons

Write a proportion.

Multiply each side by 48.

Simplify.

Answer: So, the area of PQRS is 108 square inches.

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 180 ft2

B. 270 ft2

C. 360 ft2

D. 420 ft2

If EFGH ~ LMNO and the area of EFGH is 40 square inches, find the area of LMNO.

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.

Use Areas of Similar Figures

Theorem 11.1

Substitution

Take the positive squareroot of each side.

Simplify.

So, the scale factor from ΔABC to ΔRTS isUse the scale factor to find the value of x.

Use Areas of Similar Figures

The ratio of correspondinglengths of similar polygonsis equal to the scale factorbetween the polygons.

Substitution

7x = 14 ● 5 Cross Products Property.

7x = 70 Multiply.

x = 10 Divide each side by 7.

Answer: x = 10

Use Areas of Similar Figures

CHECK Confirm that is equal to the scalefactor.

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 3 inches

B. 4 inches

C. 6 inches

D. 12 inches

The area of ΔTUV is 72 square inches. The area ofΔNOP is 32 square inches. If ΔTUV ~ ΔNOP, use the scale factor from ΔTUV to ΔNOP to find the value of x.

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?

Understand The sides of the skyscraper and thescale model are similar. You need tofind the scale factor from theskyscraper to the scale model.

Plan The ratio of the areas of the sides ofthe two figures is equal to the square ofthe scale factor between them. Beforecomparing the two areas, write them sothat they have the same units.

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 ft2

Scale Models

Theorem 11.1

Substitution

1.54 ● 10–5 = k2 Simplify using a calculator.

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.

Scale Models

CHECK Multiply 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.

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

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?