The smallest square has an area of 1, so it has a side of length 1.

You have two small squares, so we have an area of 2.

The square on top of them has a side of length 2, so has an area of 4.

The square to the left has a side of length 3, so has an area of 9.

And so on until we have the largest square having a side of length 8.

So the area is:

1 + (1 + 2^2 + 3^2 + ... + 8^2)

= 1 + (1 + 4 + 9 + 16 + 25 + 36 + 49 + 64)

= 205

-Dan