M2: Centres of Mass

Hi there, i'm really having a struggle with question 3 of this exam paper:
http://ocr.org.uk/Images/62242-question-paper-unit-4729-mechanics-2.pdf
The mark scheme is very vague as is the textbook we use, therefore I would really appreciate some guidance as to the method I should be using. Many thanks in advance!

have been taught how to do this type of problem in particular way?

From what I remember of learning it, we either used moments or weighted averages. Any method would be extremely useful for me to be honest It is rather confusing to me

The position of the centre of mass of a uniform object, which is composed of multiple parts, can be calculated as the mean position of the centres of mass of the individual parts.

The square and the equilateral triangle are both symmetrical shapes.

Can you go from there?

I did quite a lot of searching on the net and that was what I thought too, but thank you. I came out with completely the wrong answer to be honest. I'll try and upload what I did and you could perhaps tell me where I went wrong?

The shape is symmetrical in one direction, right? So the centre of mass will be somewhere along the line of symmetry.

Thanks, i'll give it another stab

Good luck I'll try to answer any questions. I'm just trying really hard to find ways of helping without giving the answer straight out

I get that, and I am grateful, I mean I don't want the answer anyway, i'm working through the paper making worked solutions for all of these for my own benefit, but the teaching for this topic, as well as my own capability in mechanics are appalling. And so I'm at a bit of a loss. Am I supposed to be taking a weighted mean of the two "centres of mass" (of the two shapes to find the actual centre) or am I wrong on that?

Try taking the line AC as x = 0.

Try taking the line AC as x = 0.