find-the-coordinates-of-the-centroids-of-the-given-figures-each-region-is-covered-by-a-thin-flat--23

Name: find the coordinates of the centroids of the given figures each region is covered by a thin flat 23
Uploaded: 2020-05-15
Duration: 2 min 7 s
Channel: Numerade
Description: 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.

Question

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.

Amanda Stone · Accepted Answer

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&#x27;m not gonna write out the zeros. And I&#x27;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&#x27;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&#x27;re dealing with the square and so all we have is six times six, which equals 36 and that&#x27;s it.

Amanda Stone · Answer

in this problem were given the coordinates negative 30 negative 38 for a and 60 and were asked to find the area and centrally of the figure. In this case, we have a trapezoid that looks like this one graft to find the century oId we just take the average of the X values in the average of the Y values given. So our X values are negative. Three native, 34 and six. And so if we plug these in, get negative three minus three plus four plus six, all divided by four. And for why Values? We have 088 and zero, and I&#x27;m just gonna write out those eighths. We get eight plus h divided by four. So if we simplify this a little bit, we get negative three minus three, which is negative. Six and six plus four, which is a positive 10. Negative. Six plus 10 equals four over four for why values a plus A is 16 and 16 will be on the top. So we&#x27;re gonna just produce this a little more. Four divided by four is equal to one and 16. Divided by four is four. And this is the center of our trapezoid. So if we come toward diagram and we go to 14 that is going to give us a value right here. So to find the area, we&#x27;re just going to use the equation for the area of a trapezoid, which is a plus B divided by two times H. And so a is our top portion here, this is B in our height. Is this value So for this trap is oId or high is eight units are A is seven units and R B is nine units. So if we use the values A equals seven b equals nine and H equals eight, we get a equals seven plus nine divided by two times eight that equals 16 divided by two times eight, which equals eight times eight, which gives us a value of 64 as our area, and that&#x27;s it.

Christopher Stanley · Answer

right here on this problem. We were told that we have a trapezoid. It has a height of two and then bases of 18 in 20. Now we need to find our area here. Area of a Travis oId is 1/2. The base is added together times your height. This is to be 1/2 18 plus 20 times two be 1/2 times 38 times two. Remember, when you multiply, order doesn&#x27;t matter. So half two is just one so just canceled. And so that just leaves us with 38 our units here. We&#x27;re meters on. So this means are areas meters squared? That&#x27;s our areas 38 square meters.

Amanda Stone · Answer

in this problem were given the coordinates negative three negative 45 negative four and 12 and were asked to find the central an area of the figure that they create. So if we graph this, we get a triangle that looks like this. And to find the century, all we need to do is take the average of the X values and the average of the Y values. So in this case, we have three terms. So we get x one plus x two plus x three, divided by three. And then why one plus? Why, too, plus why three divided by three. So if we put in our values, we see that our X values are negative. Three, five and one. So we just plug those in negative three plus five plus one divided by three. And then our why values are negative for negative four and two. So you get negative for minus four plus two all over three. So if we simplify this negative three plus five is two and two plus one is three. So we get 3/3 and then negative four minus four is negative. Eight and negative. Eight plus two is negative. Six sweet. Get negative. Six over three. So if we simplify these numbers, 3/3 is one and negative. 6/3 is negative two, and this will be our central. So if we put this into our figure, our central oId is gonna end up being right here at that point. So to find the area, the formula for the area of a triangle is a equals 1/2 base times height. If we go toward diagram, you&#x27;ll notice that are height. It&#x27;s six in her base is eight. So our basis equal to eight and her height is equal to six. So if we plug these values into our equation, we get a equals 1/2 times, eight time six and this equals 1/2 times 48 which equals 24 and that&#x27;s it.

Amanda Stone · Answer

in this problem were given the coordinates negative to zero negative to negative four, 40 and seven negative four and were asked to find the central an area of this figure. So if we graft this, we get a trapezoid that looks like this. And to find this century, we take the average of the X values an average of the Y values. So in this case, are X values are negative to negative 24 and seven. So if we plug this in, we get native to minus two plus four plus seven, divided by four. And if we do the same thing for y values, we get our Y values as zero negative 40 and negative four. So we just have zero minus four plus zero minus four, divided by four. So if we reduce this a little bit negative two minus two is negative. Four four plus seven is 11 s. We have negative four plus 11. Which leaves us with 7/4 and for why Value? We just have negative for minus four, which is negative h over four. So if we reduce this, we can&#x27;t reduce our X value 7/4. So we just leave that, as is negative 8/4 also equals negative too. And this is the central oId. So if we go back to our diagram and we go to 7/4 and go down negative too, it&#x27;s gonna be about right there, and that is going to be the center of our diagram. To find the area, we&#x27;re just going to use the equation for the area of a trapezoid, which is a plus B over two times H where a is this hop portion of our trapezoid. B is the bottom, and H is our height. In this case, A is equal to six. B is equal to nine and H is equal to four. So if we plug these values for A B and H into our equation, we get a equals six plus nine over two times four, which equals 15/2 times 4/1. So we can cancel out to from these two terms, and we&#x27;re left with 15 times to which equals 30 as our area, and that&#x27;s it

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