The effect of enlargement on the area of a shape
I can understand the effect of an enlargement on the area of a shape.
The effect of enlargement on the area of a shape
I can understand the effect of an enlargement on the area of a shape.
Lesson details
Key learning points
- An enlargement means the object and image are similar.
- All lengths in the object have been multiplied by the scale factor.
- Using index laws, this means the area has been multiplied by the scale factor squared.
Common misconception
If the length of an image is 4 times as long as its object, then its area will also be 4 times as big.
If the scale factor between lengths is 4, then the area of the image will be 16 times as big. The scale factor between the length of an object and image is different to the multiplier that shows how the area of an object changes after enlargement.
Keywords
Similar - Two shapes are similar if the only difference between them is their size. Their side lengths are in the same proportions.
Invariant - A property of a shape is invariant if that property has not changed after the shape is transformed.
Enlargement - Enlargement is a transformation that causes a change of size.
Scale factor - A scale factor is the multiplier between similar shapes that describes how large one shape is compared to the other.
Licence
This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).
Video
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Starter quiz
6 Questions
Exit quiz
6 Questions
Linear scale factor: $$3$$ -
Area scale factor: $$9$$
Linear scale factor: $$\frac{1}{2}$$ -
Area scale factor: $$\frac{1}{4}$$
Linear scale factor: $$2$$ -
Area scale factor: $$4$$
Linear scale factor: $$4$$ -
Area scale factor: $$16$$
Linear scale factor: $$\frac{3}{2}$$ -
Area scale factor: $$\frac{9}{4}$$
Linear scale factor: $$\frac{2}{3}$$ -
Area scale factor: $$\frac{4}{9}$$
