The effect of enlargement on the perimeter of a shape | Maths

Starter quiz

Two variables are in direct proportion if they have a constant ______ relationship.

'multiplicative' ✓
Some Oak pupils are discussing this graph. Which pupils are correct?

Alex: It shows direct proportion because it is increasing.

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.
The ratio table shows the conversion €7 (Euros) = £6 (Pounds Sterling). €350 = £______

'300' ✓
The perimeter of an octagon is 88 800 cm. Which calculation shows its perimeter in metres?

88 800 cm ÷ 10

88 800 cm ÷ 100 ✓

88 800 cm ÷ (8 × 100)

88 800 cm ÷ 100 ÷ 100 ÷ 100
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.

Arc length = 4π cm

Arc length = 6π cm ✓

Area = 18π cm²

Area = 36π cm²

Area = 54π cm² ✓
The area of a triangle is 3400 cm². The area of the triangle in metres squared is ______ m².

'0.34' ✓

Exit quiz

A ______ factor is the multiplier between similar shapes that describes how large one shape is compared to the other.

'scale' ✓
This sector is enlarged by scale factor 2. The angle in the image is ______°.

'60' ✓
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.

20 cm

22 cm

44 cm

60 cm

66 cm ✓
A pentagon has a perimeter of 60 cm. The pentagon is enlarged by scale factor 4. The perimeter of the image is ______ cm.

'240' ✓
$The object is enlarged by a scale factor of <Math>\frac{1}{3}</Math> to make the image. What is the perimeter of the image?$

The object is enlarged by a scale factor of $\frac{1}{3}$ to make the image. What is the perimeter of the image?

10.9 cm

11 cm

21.8 cm

22 cm ✓
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.

'37.5' ✓

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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.
By the distributive law, this means the perimeter has been multiplied by the scale factor.

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.

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.