New
New
Year 10
Higher

The effect of enlargement on the area of a shape

I can understand the effect of an enlargement on the area of a shape.

New
New
Year 10
Higher

The effect of enlargement on the area of a shape

I can understand the effect of an enlargement on the area of a shape.

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Lesson details

Key learning points

  1. An enlargement means the object and image are similar.
  2. All lengths in the object have been multiplied by the scale factor.
  3. Using index laws, this means the area has been multiplied by the scale factor squared.

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.

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.

The term "scale factor" usually refers to the "linear scale factor", a scale factor that shows the multiplicative relationship between two corresponding lengths on two similar shapes. However, it is important to evaluate whether "scale factor" means "linear" or "area" scale factor in context.
Teacher tip

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).

Lesson video

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6 Questions

Q1.
A scale factor is the multiplier between __________ shapes that describes how large one shape is compared to the other.
congruent
Correct answer: similar
transformed
Q2.
This sector is enlarged by scale factor $$\frac{1}{2}$$. The angle in the image is °.
An image in a quiz
Correct Answer: 60
Q3.
Each square on this coordinate grid is 1 unit long. This object is enlarged by a scale factor of 4 to make its image. Calculate the perimeter of the image.
20 cm
22 cm
66 cm
80 cm
Correct answer: 88 cm
Q4.
A pentagon has a perimeter of 60 cm. The pentagon is enlarged by scale factor 7. The perimeter of the image is cm.
Correct Answer: 420, 420 cm
Q5.
The object is enlarged by a scale factor of $$\frac{1}{3}$$ to make the image. What is the perimeter of the image?
An image in a quiz
9.9 cm
10 cm
18.8 cn
Correct answer: 20 cm
22 cm
Q6.
A shape is enlarged by a scale factor of $$\frac{3}{2}$$ to make its image. The perimeter of the image is 42 cm. The perimeter of the object is cm.
Correct Answer: 28, 28 cm

6 Questions

Q1.
A pentagon is enlarged by scale factor 2. What properties of the pentagon and its image are invariant?
Correct answer: angles
area
perimeter
side lengths
Correct answer: line symmetry
Q2.
Rectangle A has been enlarged to create rectangle B. Select the correct statements.
An image in a quiz
Correct answer: The perimeter of rectangle B is 3 × the perimeter of rectangle A
The perimeter of rectangle B is 9 × the perimeter of rectangle A
The area of rectangle B is 3 × the area of rectangle A
The area of rectangle B is 6 × the area of rectangle A
Correct answer: The area of rectangle B is 9 × the area of rectangle A
Q3.
Rectangle A has been enlarged to create rectangle B. The area of rectangle B is cm²
An image in a quiz
Correct Answer: 288
Q4.
Trapezium B is an enlargement of trapezium A. Calculate the area of trapezium B.
An image in a quiz
40 cm²
80 cm²
120 cm²
Correct answer: 160 cm²
200 cm²
Q5.
Match each linear scale factor to the area scale factor.
Correct Answer:Linear scale factor: $$3$$,Area scale factor: $$9$$

Area scale factor: $$9$$

Correct Answer:Linear scale factor: $$\frac{1}{2}$$,Area scale factor: $$\frac{1}{4}$$

Area scale factor: $$\frac{1}{4}$$

Correct Answer:Linear scale factor: $$2$$,Area scale factor: $$4$$

Area scale factor: $$4$$

Correct Answer:Linear scale factor: $$4$$,Area scale factor: $$16$$

Area scale factor: $$16$$

Correct Answer:Linear scale factor: $$\frac{3}{2}$$,Area scale factor: $$\frac{9}{4}$$

Area scale factor: $$\frac{9}{4}$$

Correct Answer:Linear scale factor: $$\frac{2}{3}$$,Area scale factor: $$\frac{4}{9}$$

Area scale factor: $$\frac{4}{9}$$

Q6.
Shape S is an enlargement an enlargement of shape R. The area of shape R is 32 cm². The area of shape S is cm².
An image in a quiz
Correct Answer: 200