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AREAS OF SIMILAR SHAPES

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

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  1. AREAS OF SIMILAR SHAPES

  2. 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.

  3. 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. 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. 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. 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

  7. 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 =

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