Spiral Area

First, you need to know that this is the Fibonacci Sequence:

$1, 1, 2, 3, 5\ldots F_n=F_{n-1}+F_{n-2}$

The only difference is each of a Fibonacci number has been squared:

$1, 1, 4, 9, 25\ldots {(F_n)}^2=(F_{n-1}+F_{n-2})^2$

In this case, $F_{n-1}$ are $\sqrt{441}=21$ and $F_{n-2}$ are $\sqrt{1156}=34$

Therefore, the final correct answer is $(21+34)^2=55^2=\large{\boxed{3025}}$

In the figure, starting from the 3rd square in the spiral, notice that the side of any square is the sum of the sides of the previous 2 squares. For example, the $169$ square (of side $13$ ) can be expressed as $8 + 5$ which is the sum of the previous 2 squares $64$ and $25$ .

Similarly, the side of the required square would be the side of the previous two squares. If you remember that the area of a square is $a^2$ where $a$ is the side length, you can notice that the previous two squares have side lengths $34 (34^2=1156)$ and $21 (21^2=441)$ . So the side would be $34 + 21 = 55$ units. Reapplying the formula for area of a square, $55^2 = 3025$ .