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Year 10
Foundation

The effect of enlargement on the perimeter of a shape

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

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New
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Year 10
Foundation

The effect of enlargement on the perimeter of a shape

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

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Share activities with pupils
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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. By the distributive law, this means the perimeter has been multiplied by the scale factor.

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

"I will get different linear scale factors if a measure corresponding lengths in cm vs inches."

Scale factors do not have dimensions, and aren't linked to specific units. If one length is 23 cm (9 inches), and a corresponding length is 69 cm (27 inches), then the scale factor between them is 3, regardless of whether we measured in cm or inches.

This lesson refers to some objects and their images not being similar to each other. Under the four transformations of: translation, rotation, reflection, and enlargement, images are always similar (or congruent) to the object. However, some different transformations do not preserve this property.
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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Starter quiz

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6 Questions

Q1.
Two variables are in direct proportion if they have a constant relationship.
Correct Answer: multiplicative
Q2.
Some Oak pupils are discussing this graph. Which pupils are correct?
An image in a quiz
Alex: It shows direct proportion because it is increasing.
Correct answer: Jacob: It doesn't show direct proportion because it is not a straight line.
Laura: It shows direct proportion because it passes through the origin.
Sam: It doesn't show direct proportion because there is no scale.
Sofia: You can't tell because you don't know what the variables are.
Q3.
The ratio table shows the conversion €7 (Euros) = £6 (Pounds Sterling). €350 = £
An image in a quiz
Correct Answer: 300
Q4.
The perimeter of an octagon is 88 800 cm. Which calculation shows its perimeter in metres?
88 800 cm ÷ 10
Correct answer: 88 800 cm ÷ 100
88 800 cm ÷ (8 × 100)
88 800 cm ÷ 100 ÷ 100 ÷ 100
Q5.
A circular sector with an angle of 60° has radius = 6 cm, arc length = 2π cm and area = 6π cm². The radius of the sector is increased to 18 cm. Find the arc length and area of the new sector.
An image in a quiz
Arc length = 4π cm
Correct answer: Arc length = 6π cm
Area = 18π cm²
Area = 36π cm²
Correct answer: Area = 54π cm²
Q6.
The area of a triangle is 3400 cm². The area of the triangle in metres squared is m².
Correct Answer: 0.34, .34

Exit quiz

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6 Questions

Q1.
A factor is the multiplier between similar shapes that describes how large one shape is compared to the other.
Correct Answer: scale
Q2.
This sector is enlarged by scale factor 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 3 to make its image. Calculate the perimeter of the image.
An image in a quiz
20 cm
22 cm
44 cm
60 cm
Correct answer: 66 cm
Q4.
A pentagon has a perimeter of 60 cm. The pentagon is enlarged by scale factor 4. The perimeter of the image is cm.
Correct Answer: 240, 240 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
10.9 cm
11 cm
21.8 cm
Correct answer: 22 cm
Q6.
A shape is enlarged by a scale factor of $$\frac{2}{3}$$ to make its image. The perimeter of the image is 25 cm. The perimeter of the object is cm.
Correct Answer: 37.5, 37.5 cm, 75/2