Angles, lengths and area · Foundation
مُقدَّم| English | المعنى |
|---|---|
| scale factor/skeɪl ˈfæktə/ | عامل المقياس |
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.
The method
- 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.
A rectangle is 8 cm by 5 cm. A triangle shares that base and height. How do their areas compare?
الصعوبة 1/5 · 100 عملة + مكافأة صغيرة عند الإكمال الأول اليوم
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.
A worked case
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.
الصعوبة 2/5 · 140 عملة + مكافأة صغيرة عند الإكمال الأول اليوم
Rectangle area=8×5=40 cm².
Where it goes wrong
- 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.
Not true: A triangle and rectangle with the same base and height have the same area. Volume scales by the cube of the length factor: doubling every length multiplies the volume by 8.
Find the area of a triangle of base 8 cm and height 5 cm.
الصعوبة 2/5 · 140 عملة + مكافأة صغيرة عند الإكمال الأول اليوم
Triangle area=8×5/2=20 cm².
Volume scales by the cube of the length factor.
الصعوبة 1/5 · 100 عملة + مكافأة صغيرة عند الإكمال الأول اليوم
True. Volume scales by the cube of the length factor: doubling every length multiplies the volume by 8.
Applying it
- Use a labelled sketch and appropriate units.
- This Foundation/Core lesson does not test area/volume scale factors or advanced circle-theorem proofs.
Find the sum of interior angles of a pentagon in degrees.
الصعوبة 2/5 · 140 عملة + مكافأة صغيرة عند الإكمال الأول اليوم
Interior-angle sum=(5-2)×180=540°.
Match each shape to its area rule.
الصعوبة 2/5 · 140 عملة + مكافأة صغيرة عند الإكمال الأول اليوم
Rectangle and triangle areas come from their dimensions; the interior-angle sum grows by 180° per extra side.
In your course
- AQA GCSE Mathematics (8300), Foundation tier, specification section 3.4.
- Paper 1 is non-calculator: keep fractions, surds and π exact and show each step. On calculator papers, still write the expression before its value.
- Scale factor: The multiplier that relates corresponding lengths in similar shapes.
- Use angle facts with a stated reason.
- Watch for: equal angles alone establish similarity, not equal size.