Expected value from points in triangle

I've been trying to figure out this problem in a book of mine. Done lots of reading but lost as to what I should be doing.

A point is chosen at random from a triangle with corners at (0, 0), (2, 0) & (1, 1). Let (X, Y) be the coordinates of the point chosen.
a) Find the joint pdf of X, Y
b) Calculate the marginal pdf's of X and Y .
c) Find the mean and variance of X.

I understand how to find joint pdf, marginals, mean and variance from an equation but I'm unsure how to start.

The joint density is uniform over the isosceles triangle, which has area 1. That's the only reasonable interpretation of "choose a point at random in the triangle".