This is a very great TIMSS question. Requires very high thinking skill ;)
Divide the square by creating your own line from Q to S.
Now you have 2 triangles.
Now look at the ice cream shape (triangle + quadrant). You can calculate half of the shaded region by calculating this :
Sector area - triangle area = half of the shaded region area
Since it is a half, what you have to do next is to multiply it with 2.
So now let's begin with the calculation :
Area of half of the shaded region :
[ (90º/360º) × (22/7) × 14² ] - [ (1/2) × 14 × 14 ]
= 154 - 98
∴ Total area of the shaded region :
= 2 × 56