If you put the slices that have been removed back into the figure, and figure out the resulting rectangle and subtract the slices, you get an answer that is easily calculated.
The square on the upper right is 6 cm high. That makes the width of the rectangle 9 + 6 = 15. The length is already known as 15. So this square is 15 by 15 = 225
The lower right triangle is a little harder to handle. The total width is 15. The height of the triangle is 6 + 6. The first 6 comes from the square that was removed. The total with is 15. So the height of the lower right triangle is 15 - 12 = 3
The answer to the square on the upper left that was removed = 6*6 = 36
The answer to the triangle on the lower right is 1/2 * 6 * 3 = 9
The total of the removed figues is 36 + 9 = 45
The area of the figure with both figures removed is 225 - 45 = 180 cm^2