Angles, lengths and area · Foundation
導入済み| English | 意味 |
|---|---|
| scale factor/skeɪl ˈfæktə/ | 相似比 |
Does volume scale like length?
- A model has lengths one third of the real object. How much smaller are its area and volume?
- This lesson studies scale factor 相似比: The multiplier that relates corresponding lengths in similar shapes.
Choose the mathematical structure
- Use angle facts with a stated reason. Similar shapes have equal corresponding angles and proportional corresponding lengths. Areas of rectangles and triangles come from their dimensions; compound shapes can be split into simpler parts.
- State the allowed inputs and units before calculating. An equation should express the relationship, not just record a calculator entry.
A rectangle is 8 cm by 5 cm. A triangle shares that base and height. How do their areas compare?
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
Rectangle area is 8×5=40 cm²; triangle area is 8×5/2=20 cm². The factor of one half is what the triangle formula carries.
Work through a checked case
- Check the result against the starting quantities. Substitute into the original relation, or compare the graph and numerical answer where appropriate.
A rectangle of length 8 cm and width 5 cm has area A=LW=40 cm². A triangle on the same base and height has area A=bh/2=20 cm². For a pentagon, the interior-angle sum is (5-2)×180=540°.
Angles, lengths and area
Use angle facts with a stated reason
Explain why the triangle has half the rectangle area when base and height match.
Find the area of a rectangle of sides 8 cm and 5 cm.
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
Rectangle area=8×5=40 cm².
Test a tempting shortcut
- Equal angles alone establish similarity, not equal size. Use corresponding lengths in the same order. Convert linear units before calculating area or volume, or square/cube the conversion factor correctly.
- When a shortcut fails, identify the assumption it breaks. Keep an exact value until the requested final rounding.
A triangle and rectangle with the same base and height have the same area. This claim is false. Explain which definition or assumption it violates.
Find the area of a triangle of base 8 cm and height 5 cm.
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
Triangle area=8×5/2=20 cm².
A triangle and rectangle with the same base and height have the same area.
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
Equal angles alone establish similarity, not equal size. Use corresponding lengths in the same order. Convert linear units before calculating area or volume, or square/cube the conversion factor correctly.
Interpret a new situation
- Use a labelled sketch and appropriate units. This Foundation/Core lesson does not test area/volume scale factors or advanced circle-theorem proofs.
- A complete solution gives the mathematical result and explains what it means. Check that it is possible in the stated context.
Find the sum of interior angles of a pentagon in degrees.
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
Interior-angle sum=(5-2)×180=540°.
Match each shape to its area rule.
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
Rectangle and triangle areas come from their dimensions; the interior-angle sum grows by 180° per extra side.
Use this in your course
- 4MA1 · Foundation · 4. Match the target tier and specification before assigning extensions.
- Give the method before the final answer, and use the paper's calculator and formula rules. Review a wrong answer by locating the first invalid step.
The multiplier that relates corresponding lengths in similar shapes. Choose the relationship, show the method, check its assumptions and interpret the result.