Not sure how to figure this problem out.

To make things easier I'm going to call the very center of the figure .

Take a look at just one quarter of the figure, say the square .
We can see that the triangle is exactly half of this square.

BUT: We could do the same thing for ANY of the four quarters, and the observation would be the same: the little triangle is exatly 1/2 of 1/4 of .

So: The 4 little triangles make up: of which simpilfies to exactly 1/2.

So we have our = 1/2 of or 121sq.ft.