In case we have a shape which is composed out of simpler shapes, for which we know properties of areas or centroidal distances, then we can calculate the corresponding area and central distance of a composite area, using the following expressions. The area can be expressed as the sum of the composing areas A_i, and the first moment of the area expressed as its centroidal distance, times the area, should be equal to the sum of the centroidal distances x_i, times A_i. Okay. Recall that the centroidal distance x, is the integral of xdA, over A. So the product x bar cross A, is the integral of xdA is what we called the first moment with respect to the y-axis, similar expressions and explanations for the y direction. Also, notice that here the notation I use is x bar, before we use the notation xc. So we use this sometimes x bar, sometimes xc. Now, let's see what we are saying here. When we have a shape like the shape shown here, which is composed of I can think of it being composed of this is a parabolic shape, with zero slope. So we have about a parabolic shape. So I can think of this as being the first part composing area. So this would be area A_1. Then next we can think having the rectangular shape shown here, we will denote this as A_2, and finally the circular area which has been cut out. Okay. So this is the area A_3. So the shape we're interested in is the shaded area, the total shaded area shown here. Which clearly is the sum A_1, plus A_2 minus A_3. So the best way to handle this is to create a table, where we have the different members, the areas of the corresponding members A_i, the centroidal distances of each of the shapes of the difference composing areas, and the first moments x_iA_i. Let's look at this particular example, for element number one, the area is, we have a parabolic shape. We have already found expressions into the area of a parabolic shape is one-third b, times h, and the centroidal distance is at three-quarters of b. Therefore, one-third, 4 times three, is equal to four. The centroidal distance is three-quarters of four, so it's equal to three, and the first moment is equal to 12. The units here are meters square. This is meters, and this is meters cube. Let's go to area two. Area two is a rectangle. The area is base times height is equal to 15. The centroid of this rectangle is at this, at the middle of five. So 2.5 plus four, gives 6.5 meters, and the product 15 times 6.5, is 97.5. Finally, area three which is the circle is pi r square, r is one. So it's pi. But it is with a minus sign because it's a negative area, because we cut this area out from the rectangle. The distance, the centroid of the circle is clearly at the center of the circle which is two meters from the right, that is seven meters from left, and minus pi times seven is, minus 21.98. We sum up all the areas. Sum of all the areas. The i is 15.86. We sum up all the affairs moments and this gives us 87.52 is the sum of x_iA_i. Based on the expression we have here, the average central distance, the centroid distance over the composite area is the ratio of 87.52 cubic meters, divided by 15.86 square meters, and this gives us 5.52 meters. So the centroid is a sum of the length of the circle, somewhere here. Okay. So this is the overall centroid, and this length is 5.52. While the entire area is the one we calculate here, 15.86 square meters.