11-5 Areas of Similar Figures

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.

Similarity, Perimeter, and Area

Rectangle ARectangle B

1.What is the length and width of each rectangle?

2.What similarity ratio was used?

3.Find the perimeter of each rectangle.

4.Find the area of each rectangle.

Similarity, Perimeter, and Area

1.What is the length of the sides of each square?

2.What similarity ratio was used?3.Find the perimeter of each square.4.Find the area of each square.

How do the similarity ratios of the polygon relate to the ratios of their

perimeters and areas?

Shape Sim ratio P-ratio A-ratio

Rectangle 2/1 2/1

4/1

Square 1/3 1/3 1/9

Pattern ( )1 ( )1 ( )2

Areas of Similar Figures

If two polygons are similar, their perimeters are proportional to their scale factor.

If two polygons are similar, their area are proportional to the square of their scale factor.

p. 818

ABCDE ~ GHIJK. The similarity ratio of ABCDE to GHIJK is 2.

A

B

CD

E H

IJ

K

G

1.If the perimeter of GHIJK is 10 cm, what is the perimeter of ABCDE?

2.If the area of ABCDE is 24 cm2, what is the area of GHIJK?

20 cm

6 cm2

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

Write a proportion.

Multiply each side by 48.

Simplify.

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.

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.

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.

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

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.

11-5 Assignment

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