Centre of Gravity Question (unsure about third shape)

[JimCrown]

Area 1 : 297 x 270 = 80190
Area 2 : 297 x 150 / 2 = 22275
Area 3 : 100 x 100 = 10000

Area Total : 80190 + 22275 + 10000 = 92465

x1 : 270 / 2 = 135
x2 : 270 + 150/3 = 320
x3 : 270 - 120 = 150

x = (80190 x 148.5) + (22275 x 198) - (10000 x 247) / 92465 = 149.772

y1 : 297 / 2 = 148.5
y2 : 297 - (297/3) = 198
y3 : 297 - 50 = 247

y = (80190 x 135) + (22275 x 320) - (10000 x 150) / 92465 = 177.945


I think I have done this correct. I am unsure about the third shape (the mini square/the one cut out) and whether I have done the centre of gravity x value and y value correct for it.

 

[Dr.Peterson]

View attachment 10742
Area 1 : 297 x 270 = 80190
Area 2 : 297 x 150 / 2 = 22275
Area 3 : 100 x 100 = 10000

Area Total : 80190 + 22275 + 10000 = 92465 <-- you meant -

x1 : 270 / 2 = 135
x2 : 270 + 150/3 = 320
x3 : 270 - 120 = 150

x = ((80190 x 148.5) + (22275 x 198) - (10000 x 247)) / 92465 = 149.772 <-- this is really y

y1 : 297 / 2 = 148.5
y2 : 297 - (297/3) = 198
y3 : 297 - 50 = 247

y = ((80190 x 135) + (22275 x 320) - (10000 x 150)) / 92465 = 177.945 <-- this is really x

I think I have done this correct. I am unsure about the third shape (the mini square/the one cut out) and whether I have done the centre of gravity x value and y value correct for it.

I don't think you wrote what you intended. You used the y_i values (not yet calculated) in your calculation of x, and vice versa. So I think you meant to say that x is 177.945 and y is 149.772. Is that right?

If so, everything you really did is correct, as far as I can see. Why are you unsure?