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Find the coordinates of the centroids of the given figures. Each region is covered by a thin, flat plate. A floodgate is in the shape of an isosceles trapezoid. Find the location of the centroid of the floodgate if the upper base is $20 \mathrm{m}$ the lower base is $12 \mathrm{m},$ and the height between bases is $6.0 \mathrm{m} .$ See Fig. 26.46.

Calculus 2 / BC

Chapter 26

Applications of Integration

Section 4

Centroids

Missouri State University

University of Michigan - Ann Arbor

Boston College

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

02:07

Find the centroid and area…

03:15

00:52

Find the area of each figu…

03:21

03:25

02:55

03:11

02:22

02:26

in this problem were given the coordinates 000660 and 66 and were asked to find the central an area of the figure. So the graft this we get a square that looks like this. And to find the central, all we have to to is take the average of the X values and the average of the Y values. And since we have four for each, we divide the access by four and the wise by four. So if we take the numbers that were given in our problem for excess, we have 006 and six. We can ignore those zeros, and we just get six plus six divided by four. And for why? Values? We have 060 and six. So the same thing. I'm not gonna write out the zeros. And I'm just gonna add our sixes and divide by four. So if we simplify this for both of these, we get 12/4 and 12/4 is the same thing as three. So we get 33 as our century. So if we go back to our diagram and we graft this, we are going to get a value or we're gonna get our point to be right there, which is the center of our square. To find the area. All we have to do is use the following equation. Area equals base times height. Since this is a square, all of our lengths are equal. This is six. Which means that our piece also has to be sick since we're dealing with the square and so all we have is six times six, which equals 36 and that's it.

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