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.