Question

If any two dimensional figure is enlarged by a scale factor of 2, the area of the enlarged figure is times the area of the original figure.

Answer 1

When we calculate area of any two dimensional figure, we use two dimensions $(\text{length}\times \text{width},\text{side}\times \text{side}...\text{etc.})$ to determine the area.

If the scale factor is $k$, then each of these two dimensions must be multiplied by $k$ to find the dimensions for the new shape.


$\therefore$ Area of new shape $=(k\times \text{length})\times (k\times \text{width})$
$=k\cdot k\times (\text{length}\times \text{width})$
$=k^2\times \left(\text{area of the original shape}\right)$

Here, the scale factor is $2$.
Hence, area of new shape
$=2^2\times \left(\text{area of the original shape}\right)$
$=4\times \left(\text{area of the original shape}\right)$