Year 10 - Maths
The effect of enlargement on the area of a shape
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit, pupils investigate the effect of an enlargement on the perimeter and area of a 2-D shape and the volume of a 3-D shape.
Lesson Summary
You will learn to understand the effect of an enlargement on the area of a shape.
Key Notes
- 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.
Vocabulary To Learn
- 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 Mistakes To Avoid
- If the length of an image is 4 times as long as its object, then its area will also be 4 times as big.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
An enlargement means the object and image are similar. All lengths in the object have been multiplied by the scale factor.
2. Use this key word in a maths sentence and explain it clearly. 'Similar'
Two shapes are similar if the only difference between them is their size. Their side lengths are in the same proportions. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: If the length of an image is 4 times as long as its object, then its area will also be 4 times as big. Correction: 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.
More Lessons In This Unit
- Checking and securing understanding of congruent triangles (ASA) Study Guide
- Checking and securing understanding of congruent triangles (RHS) Study Guide
- Checking and securing understanding of congruent triangles (SAS) Study Guide
- Checking and securing understanding of congruent triangles (SSS) Study Guide
- Checking and securing understanding of direct proportion in context Study Guide
- Problem solving with advanced similarity knowledge Study Guide
- Problem solving with similarity Study Guide
- The effect of enlargement on the perimeter of a shape Study Guide
- The effect of enlargement on the volume of a 3D shape Study Guide
- Using the scale factor for enlarging a volume Study Guide
- Using the scale factor for enlarging an area Study Guide
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