Answer
$\frac{1}{3}$
Work Step by Step
The total area can be represented by the sum of the infinite geometric series with first term $a_1=0.25$ and common ratio $r=0.25$. An infinite geometric series converges if and only if $|r|\lt1$, where $r$ is the common ratio. If it converges, then it equals $\frac{a_1}{1-r}$ where $a_1$ is the first term.
Here $0.25\lt1$.
Hence the sum: $\dfrac{0.25}{1-0.25}=\frac{1}{3}$