**Area and Enlargements**

Starter

Example

**L.O. - To understand the relationship**

between the scale factor of an enlargement and the area of the enlarged shape.

between the scale factor of an enlargement and the area of the enlarged shape.

(a) What is the scale factor of the enlargement from the small shape to the large.

(b) Find the area of the small shape.

(c) Find the area of the large shape.

(d) How many times bigger is the area of the large shape than the small?

Starter

(a) What is the scale factor of the enlargement from the small shape to the large.

Scale factor 2.

(b) Find the area of the small shape.

1 cm

(c) Find the area of the large shape.

4 cm

(d) How many times bigger is the area of the large shape than the small?

4

2

2

Area Scale Factor

If the length scale factor is B, the area scale factor is B .

2

i.e. if you times the lengths by B you times the area by B .

2

Using the Area Scale Factor

6 cm

7 cm

Area of rectangle =

If the shape is enlarged by scale factor 3 what will be the new area?

Using the Area Scale Factor

6 cm

7 cm

Area of rectangle =

42 cm

If the shape is enlarged by scale factor 3 what will be the new area?

Length scale factor = 3, so area factor = 9.

9 x 42 = 378 cm .

2

2

Example

12 cm

5 cm

Area of Triangle =

(Don't forget to half it).

If the shape is enlarged by scale factor 5, what

will the area of the new shape be?

Example

12 cm

5 cm

Area of Triangle =

(Don't forget to half it).

If the shape is enlarged by scale factor 5, what

will the area of the new shape be?

30 cm

Length scale factor = 5, so Area scale factor = 25.

Area = 30 x 25 = 750 cm

2

2

Area of small shape:

Scale factor of enlargement:

Area of enlarged shape:

Example

Area of small shape:

Scale factor of enlargement:

Area of enlarged shape:

**Worked Example**

**Worked Example**

**Worked Example**

Main Activity

Choose red shapes, amber shapes or green shapes.

Find the area of the shape.

Then find the area of the shape when it is enlarged by the given scale factor.

Area = 9 Area = 24 Area = 35 Area = 25

Enlarged = 36 Enlarged = 216

Enlarged = 560 Enlarged = 2500

Area = 35 Area = 30 Area = 70 Area = 28

Enlarged = 560 Enlarged = 750

Enlarged = 700 Enlarged = 7

Area = 64 Area = 12 Area = 20 Area = 0.25

Enlarged = 1024 Scale factor = 3

Enlarged = 5 Enlarged = 0.4375

= 9/16

Plenary

Area = 36 cm

Area = 9 cm

2 cm

Find the dimensions of the large

rectangle.

Plenary

Area = 36 cm

Area = 9 cm

2 cm

Find the dimensions of the large

rectangle.

4 by 9 rectangle.

**Activities**

**Activity**

Answers

Answers

**Key**

Examples

Examples