What are similar shapes?
Two shapes are Mathematically Similar if one is an enlargement of the other.
Equivalent Angles in the two shapes will be equal.
Equivalent Lengths in the two shapes will be in the same ratio and are linked by a Scale Factor (which you will normally have to find).
Equivalent Areas are linked by an Area Factor (see below).
Equivalent Volumes are linked by a Volume Factor (see below).
Working with similar shapes
- Identify equivalent known quantities (Lengths, Areas or Volumes).
- Establish direction (getting bigger or smaller?).
- Find Scale/Area/Volume Factor = Second Quantity ÷ First Quantity
(Check Factor > 1 if getting bigger and Factor < 1 if getting smaller.)
- Convert between Scale/Area/Volume Factors using
Area Factor = (Scale Factor)2 ( Scale Factor = √(Area Factor) )
Volume Factor = (Scale Factor)3 ( Scale Factor = ∛(Volume Factor) )
- Use Scale/Area/Volume Factor to find new quantity