What is an enlargement?
An enlargement is a transformation that changes the size of a figure while keeping its shape. It is described by two things: a centre of enlargement (a fixed point) and a scale factor $k$. The image and object are similar figures.
Scale factor
Each image length is $k$ times the matching object length:
Key formula
$\text{image length}=k\times\text{object length},\qquad \text{area factor}=k^2$
If $k>1$ the figure gets larger; if $0
Area factor
Because area involves two dimensions, the area is multiplied by $k^2$, not by $k$. So a scale factor of $3$ makes lengths $3$ times as long but areas $9$ times as large.
Example
A triangle of area $5\text{ cm}^2$ is enlarged by scale factor $3$. Its image has area $5\times 3^2=5\times 9=45\text{ cm}^2$.
Remember
To find the scale factor from areas, take the square root of the area factor: $k=\sqrt{\text{area factor}}$.