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Similar Lengths
How do I work with similar lengths?- Equivalent lengths in two similar shapes are connected by a scale factor, indicating that they are in the same ratio.
- Typically, the initial step involves determining the scale factor.
- Step 1: Recognize equivalent known lengths.
- Step 2: Establish the direction of change:
- If the scale factor is greater than 1, the shape is enlarging.
- If the scale factor is less than 1, the shape is shrinking.
- Step 3: Calculate the scale factor by dividing the second length by the first length.
- Step 4: Utilize the scale factor to ascertain the required length.
Similar Areas & Volumes
What are similar shapes?
- Two shapes are mathematically similar if one is an enlargement of the other.
- If two similar shapes are linked by the scale factor, k
- Equivalent areas are linked by an area factor, k2
- Equivalent volumes are linked by a volume factor, k3
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Similar Shapes
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How do I work with similar shapes involving area or volume?
- Step 1: Identify the equivalent known quantities
- These could be for lengths, areas or volumes
- Step 2: Establish direction
- Are they getting bigger or smaller?
- Step 3: Find the Scale Factor from two known lengths, areas or volumes
- Second Quantity ÷ First Quantity
- Check the scale factor is > 1 if getting bigger and < 1 if getting smaller
- If the scale factor, s.f., is from two lengths, write it as k = s.f.
- If the scale factor, s.f., is from two areas, write it as k2 = s.f.
- If the scale factor, s.f., is from two volumes, write it as k3 = s.f.
- Step 4: Use the value of the scale factor you have found to convert other corresponding lengths, areas or volumes using
- Area Scale Factor = (Length Scale Factor)2
- Or Length Scale Factor = √(Area Scale Factor)
- Volume Scale Factor = (Length Scale Factor)3
- Or Length Scale Factor = ∛(Volume Length Factor)
- Area Scale Factor = (Length Scale Factor)2
- Use the scale factor to find a new quantity
Question for Similar Shapes
Try yourself:
What is the first step to working with similar lengths?View Solution
The document Similar Shapes | Mathematics for GCSE/IGCSE - Year 11 is a part of the Year 11 Course Mathematics for GCSE/IGCSE.
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FAQs on Similar Shapes - Mathematics for GCSE/IGCSE - Year 11
| 1. What are the characteristics of shapes with similar lengths? |  |
| 2. How does having similar areas benefit in geometry? | |
Ans. Having similar areas allows for easier comparisons between different shapes, as the size of the area remains proportional even if the shapes are scaled up or down.
| 3. Can shapes with similar volumes have different dimensions? | |
Ans. Yes, shapes with similar volumes can have different dimensions. As long as the volume remains the same, the shapes can vary in size and shape.
| 4. What are the key differences between shapes with similar areas and shapes with similar volumes? | |
Ans. Shapes with similar areas have equal surface areas, while shapes with similar volumes have equal space occupied within them.
| 5. How can one determine if two shapes are similar in geometry? | |
Ans. Two shapes are considered similar if their corresponding angles are equal and their sides are proportional in length. This can be confirmed through calculations and measurements.
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About this Document
Apr 29, 2025
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Document Description: Similar Shapes for Year 11 2025 is part of Mathematics for GCSE/IGCSE preparation.
The notes and questions for Similar Shapes have been prepared according to the Year 11 exam syllabus. Information about Similar Shapes covers topics
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