hi dgiroux48

Welcome to the forum.

For 1, I'd divide the triangle into horizontal parallel strips. (see diagram below)

I assume you can use the property 'centre of mass of a thin strip' lies at its centre. If not you'd have to prove that first.

So for each strip the C of M lies on the median at a vertical distance from the x axis, y, that is proportional to its length, L.

(That comes straight from a Euclidean theorem)

So you can integrate in the y direction.

Bob

ps. I'll come back to the Moment of Inertia later.