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 answer:

= 1/2 of

or 121sq.ft.