# Centroids please need a bit of help

1. Aug 8, 2010

### mratwi36

I'm not sure wether the top shape triangle the x axis should be minus or plus.
i've got all the areas including x1 x2 x3 x4 and y1 y2 y3 y4 since i've splited the whole shape into 4 shapes (2 triangle and 1 square and 1 rectangle).would appreaciate if any one can help me out with it.

http://i21.photobucket.com/albums/b283/NMchugh/Various/centroids.png

2. Aug 8, 2010

### rock.freak667

If you are taking the first moment of area about the x-axis, then all the y-coordinates above the x-axis is positive, and all the ones below are negative.

Similarly, about the y-axis, everything to the right, x-coords are positive, negative to the left.

Try it and post your working.

3. Aug 8, 2010

### mratwi36

what i did is 4 shapes
shape 1)
Top Triangle Area=1890 mmsq x=42 y=10
Shape 2)
Left Square Area=2916 mmsq x=-27 y=27
Shape 3)
Right rectangle Area=3888 mmsq x=27 y=36
Shape 4)
Bottom Triangle Area=1728 mmsq x=24.3 y=-16

Sum of all areas = 10422 mmsq
Sum of all x= 66.3
Sum of all y= 57
x=Sum of all x/Sum of A = 66.3/10422=6.3x10^-3
y=57/10422= 5.5x10^-3

is this answer correct this is what i solve first time and answers aswell but the problem is i got lst with the top triangle as half of it goes threw the first quadrent which is positive and the other half goes threw the second one which would give out x as negative and y as positive.

4. Aug 8, 2010

### rock.freak667

The formula for the x centroid is this

$$A \bar{x}=A_1x_1+A_2x_2+A_3x_3+...$$

xn is the distance of the centroid of the individual areas An from the axis you are taking it about.

5. Aug 8, 2010

### mratwi36

oh yeah sorry stupid mistake.

i got x=14.1
and y= 20.1

6. Aug 10, 2010

### vela

Staff Emeritus
I got x=19.3 mm and y=26.6 mm.

This is obviously wrong because y should be inside the triangle which is above the line y=54 mm. I don't get the same value for x.
Looks like you swapped x and y for the rectangle.
Your value for x is wrong.

Last edited: Aug 10, 2010
7. Aug 10, 2010

### mratwi36

shape 1)
Top Triangle Area=1890 mmsq x=42 y=10
This is obviously wrong because y should be inside the triangle which is above the line y=54 mm. I don't get the same value for x.

welll what i've done is based on the diagram is 54+72= 126 which is the base of the triangle divided by three would give you 42 for x. and y = 30/3 = 10 mm

Shape 3)
Right rectangle Area=3888 mmsq x=27 y=36 (yeah i fixed those yesterday)

Shape 4)
Bottom Triangle Area=1728 mmsq x=24.3 y=-16 x=24(this is the number i got)the .3 was when i first posted this thread.

and then A1X1+A2X2+A3X3+A4X4 / (divided) A1+A2+A3+A4 = 182088/10422 = 17.5

y= 16.8

8. Aug 10, 2010

### vela

Staff Emeritus
You're given a coordinate system to work with, and you need to find the coordinates of the centroid of each region in that coordinate system. It's those values that go into the formula rock.freak mentioned.

The number 126/3 gives you the distance of the centroid from the right edge of the top triangle, and the number 30/3 gives you the distance above the bottom edge of the top triangle. What are the coordinates of that point?