AREAS OF SIMILAR SHAPES

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# AREAS OF SIMILAR SHAPES - PowerPoint PPT Presentation

AREAS OF SIMILAR SHAPES. enlarge with a length scale factor of 2. 2 cm. 1 cm. 4 cm. 2 cm. The diagram shows that: If the length scale factor is 2, then the area scale factor is 4. enlarge with a length scale factor of 3. 1 cm. 3 cm. 2 cm. The diagram shows that:

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### AREAS OF SIMILAR SHAPES

enlarge with a length

scale factor of 2

2 cm

1 cm

4 cm

2 cm

The diagram shows that:

If the length scale factor is 2, then the area scale factor is 4.

enlarge with a length

scale factor of 3

1 cm

3 cm

2 cm

The diagram shows that:

If the length scale factor is 3, then the area scale factor is 9.

6 cm

General rule:

If the length scale factor is k, then the area scale factor is k2.

Examples

1

The two shapes are similar.

The area of the smaller shape is 5 cm2.

Find the area of the larger shape.

3 cm

6 cm

Length scale factor =

Area scale factor =

Area of larger shape =

Examples

2

The two shapes are similar.

The area of the larger shape is 13.5 cm2.

Find the area of the smaller shape.

4 cm

12 cm

Length scale factor =

Area scale factor =

Area of smaller shape =

Examples

3

The two shapes are similar.

The area of the smaller shape is 12 cm2.

The area of the larger shape is 27 cm2.

Find the value of x.

4 cm

x cm

Area scale factor =

Length scale factor =

So x =

C

Examples

4

Area of triangle CDE = 10 cm2.

a Calculate the area of triangle ABC.

b Calculate the area of ABDE.

4 cm

E

D

2 cm

A

B

C

a

Triangles ABC and EDC are similar.

Length scale factor =

6 cm

Area scale factor =

A

B

Area of triangle ABC =

C

4 cm

b

Area of ABDE = area of Δ ABC − area of Δ CDE

E

D

D

E

Examples

5

Find the area of triangle CDE.

15 cm

C

21 cm

147 cm2

B

A

C

Triangles ABC and EDC are similar.

15 cm

D

E

Length scale factor =

C

21 cm

147 cm2

Area scale factor =

B

A

Area of triangle CDE =