Center of mass to find support reactions at pins for a homogeneous flat plate

[musicmar]

Homework Statement

The mass of the homogeneous flat plate is 50 kg. Determine the reactions at the supports A and B. I've attached the diagram.

The Attempt at a Solution

I know I will need to find the center of mass. I don't remember exactly how to do it, but I found the centroid location first by using composite areas and the formula xbar=∑(x^~)A/∑A and similar for y.
I found the centroid location to be at (0.566,0.183) m.

I have two questions.
If I find the center of mass, do I then just treat the mass as a concentrated load at that point horizontally and find the reactions using the moment about A or B and the sum of the forces in the y?
Can someone point me in the right direction for finding the center of mass from here?

Thank you!

 

[musicmar]

I think I figured it out. I didn't need to do anything beyond finding the centroid location to find the support reactions. I got an answer of By= 198 N and Ay = 292 N

 

[rude man]

You got it. But they made finding the centroid a bit of an exercise, eh?