Questions about the scale factors of lengths, areas and volumes of similar shapes.
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Level 1 - Lengths of similar shapes
Level 2 - Areas of similar shapes
Level 3 - Volumes of similar shapes
Level 4 - Mixed questions
Level 5 - Exam-style questions
If you enlarge the dimensions of a polygon by multiplying them by a number (scale factor), the area is increased by the square of that factor.
For example if the sides of a rectangle are enlarged by a factor of 6, the area of the rectangle increases by a factor of 62
If the length of the original rectangle was 5cm and the width was 2cm then after enlargement they would be 30cm and 12cm respectively.
The area of the original rectangle is 5cm x 2cm = 10cm2
The area of the enlarged rectangle is 30cm x 12cm = 360cm2
As you can see the area of the enlarged rectangle is 62 times larger than the area of the original rectangle.
The same can be shown for any polygon when enlarged.
Enlargement by a fractional scale factor is equivalent to the shape reducing in size.
If you enlarge the dimensions of a three dimensional shape by a scale factor, the volume is increased by the cube of that factor.
For example if the sides of a cuboid are enlarged by a factor of 6, the volume of the cuboid increases by a factor of 63