First figure: A circle's area is calculated as pi*r^2, so a semicircle is pi*r^2 / 2,
and a quarter circle is pi*r^2 / 4. A triangle's area is
0.5*base*height. We have a quarter circle of radius 12, of which the area is pi*(12^2 / 4) = 36pi. The area of the triangle ABC is 0.5*12*12 = 72, so the shaded area is 36pi - 72.
Second figure: Rather than having to add and subtract the measurements of the semi-circle, notice that the semicircle to the left of AD is actually identical in area to the blank semicircle-shaped space to the left of BC. So if we transferred the red semicircle into the blank space, we would end up with a square of side length 24 cm. The area of a square is s^2 = 24^2 = 676 cm^2.
The third and fourth images seem to be duplicates of the first two.
