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Scale Factor effects on Perimeter and Area
供稿人: Jennings
(原作者: Cason)

The ratio of the lengths of corresponding sides in

similar figures (same shape but different size) is

called scale factor.  It may be expressed as a

fraction, decimal, percent, or whole number. 

 

The scale factor from Fig A to Fig B is 3/6  = ½.

The scale factor from Fig B to Fig A is 6/3 = 2

         6 cm                 3 cm
Fig A
Fig B

 

A rectangle has sides of 3 cm and 5 cm.  A similar

rectangle is dilated with a scale factor of ½.  Find its

length and width.

6 cm by 10 cm

2 cm by 3 cm

1.5 cm by 2.5 cm

2 cm by  2.5 cm

 

A rectangle has sides of 3 cm and 5 cm.  A similar

rectangle is dilated by a scale factor of 2.  Find its

dimensions.

6 cm by 10 cm

2 cm by 3 cm

1.5 cm by 2.5 cm

2 cm by  2.5 cm

If we know one shape's perimeter and the scale factor,

we can find the other shape's perimeter by multiplying

the original perimeter by the scale factor.  If the first

shape has a perimeter of 16 cm and is dilated by a

scale factor of ½, the second shape's perimeter is...

Perimeter = 16

80 cm

5

32 cm

3

8 cm

2.5

80 cm

1.5

If the perimeter is of a shape is 16 cm and is

dilated with scale factor of 2, the perimeter

of the similar shape is...

8 cm

5

32 cm

3

80 cm

3200 cm

45 square centimeters

32 square centimeters

Since area is measured in square units, the scale

factor needs to be squared before multiplying it by

the area of the first shape to find the area of the

dilation.  Our original shape is 3 cm by 5 cm. 

Therefore the area is 3 x 5 or 15 square centimeters. 

A similar shape dilated with a scale factor of 3 will

have an area of...

5
3

90 square centimeters

135 square centimeters

5(3)
3(3)

If the original area of a shape is 32 square

centimeters and is dilated by a scale factor of ¼,

the new shape's area would be...

8
8

2 square cm

4 square cm

32 square cm

64 square cm

8(¼)
8(¼)

The formula for the circumference of a circle

C=2∏r  when ∏=3.14.  Find the circumference of a

circle with a radius of 2 inches dilated by a scale

factor of 3.

C=2(3.14)(2)

C=12.56

2
C=2(3.14)(        )
C =

The area of a rectangle is 12 inches squared. 

The rectangle is dilated by a scale factor of ½. 

What is the area of the new rectangle?

inches squared

The perimeter of a triangle is 9 cm.  The

triangle is dilated by a scale factor of 2. 

Find the perimeter of the new triangle.

cm

The area of a square is 64 square inches. 

The square is dilated by a scale factor of 2. 

What is the area of the new square?

square inches

Figure A is dilated creating Fig B. 

 

What is the scale factor from Fig A to Fig B?

 

What is the perimeter of Fig B?

 

What is the area of Fig B?

Fig A
9
9

Fig B

square units
3
units
3

Figure A is dilated creating Fig B. 

 

What is the scale factor from Fig A to Fig B?

 

What is the perimeter of Fig A?

 

What is the perimeter of Fig B?

Fig A
3
3

Fig B

9
square units
units
9

Figure A is dilated creating Fig B. 

 

What is the scale factor from Fig A to Fig B?

 

What is the area of Fig A?

 

What is the area of Fig B?

Fig A
3
3

Fig B

square units
square units
9
9

A rectangle is dilated with a scale factor of 3. 

Which statement correctly describes the perimeter

of the new figure?

 The new perimeter is 1/9 times the original

 The new perimeter is 1/3 times the original

 The new perimeter is 3 times the original

 The new perimeter is 9 times the original

A rectangle is dilated with a scale factor of 3. 

Which statement correctly describes the area

of the new figure?

 The new area is 1/9 times the original

 The new area is 1/3 times the original

 The new area is 3 times the original

 The new area is 9 times the original

A rectangle is dilated with a scale factor of ⅓. 

Which statement correctly describes the area

of the new figure?

 The new area is 1/9 times the original

 The new area is 1/3 times the original

 The new area is 3 times the original

 The new area is 9 times the original

A rectangle is dilated with a scale factor of ⅓. 

Which statement correctly describes the perimeter

of the new figure?

 The new perimeter is 1/9 times the original

 The new perimeter is 1/3 times the original

 The new perimeter is 3 times the original

 The new perimeter is 9 times the original

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