The problem asks to convert an area of $2.25 \, m^2$ to $dm^2$.

1. Problem Description

The problem asks to convert an area of $2.25 \, m^2$ to $dm^2$.

2. Solution Steps

We know that 1 meter (m) is equal to 10 decimeters (dm).

Therefore, $1 \, m = 10 \, dm$.

To convert square meters ($m^2$) to square decimeters ($dm^2$), we need to square the conversion factor:

$1 \, m^2 = (1 \, m)^2 = (10 \, dm)^2 = 100 \, dm^2$.

So, to convert $2.25 \, m^2$ to $dm^2$, we multiply by 100:

$2.25 \, m^2 = 2.25 \times 100 \, dm^2$.

$2.25 \times 100 = 225$.

3. Final Answer

$2.25 \, m^2 = 225 \, dm^2$.