AREAS OF SIMILAR SHAPES

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.

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 =

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 =

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 =

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

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 =