1. AREAS OF SIMILAR SHAPES

2. The diagram shows that:
enlarge with a length
scale factor of 2
4 cm
2 cm
2 cm
1 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
6 cm
3 cm
2 cm
1 cm
The diagram shows that:
If the length scale factor is 3, then the area scale factor is 9.
General rule:
If the length scale factor is k, then the area scale factor is k2.

3. The two shapes are similar. The area of the smaller shape is 5 cm2.
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 =

4. The two shapes are similar. The area of the larger shape is 13.5 cm2.
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 =

5. The two shapes are similar. The area of the smaller shape is 12 cm2.
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 =

6. Area of triangle CDE = 10 cm2. a Calculate the area of triangle ABC.
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
6 cm A B C a
Triangles ABC and EDC are similar.
Length scale factor =
Area scale factor =
Area of triangle ABC =
4 cm E D C b
Area of ABDE = area of Δ ABC − area of Δ CDE

7. Find the area of triangle CDE.
Examples 5
Find the area of triangle CDE.
15 cm C
21 cm
147 cm2 A B D E C
15 cm
Triangles ABC and EDC are similar.
Length scale factor = A B C
21 cm
147 cm2
Area scale factor =
Area of triangle CDE =