Area of the square = (side)*(side)
Area of the square = (2)*(2)
Area of the square = 4
Area of the quarter circle = (area of full circle)/4
Area of the quarter circle = (pi*r^2)/4
Area of the quarter circle = (pi*1^2)/4
Area of the quarter circle = (1/4)*pi
The top shaded region is found by taking the area of the square and subtracting off the area of the quarter circle, so we get,
top shaded region area = (area of square) - (area of quarter circle)
top shaded region area = (4) - (1/4pi)
The two shaded regions are congruent so we can double the area of the top region to get the total overall area.
Total shaded area = 2*(top shaded region area)
Total shaded area = 2*(4 - pi/4)
Total shaded area = 8 - pi/2
Total shaded area = 8 - (1/2)pi
Therefore, the final answer is [tex]8 - \frac{1}{2}\pi[/tex]
