for part (a), a shorter method is to visualize that you shifted the shaded quarter circle in square 1 (as labelled in my picture) to white space in square 4 (like completing jigsaw puzzle). so the equation for the total area will be: area of square 4 + area of semicircle + (area of square 3 - area of smaller quarter circle).

for part (b), after finding the circumference values for the large quarter circle, the semicircle and the smaller quarter circle, you insert the values into this equation to get the total perimeter: 2x(circum. of large quarter circle) + radius of large quarter circle + circum. of semicircle + 2x4 + circum. of smaller quarter circle.