I don't think there is any easy way to explain these. There is a proof of the area formula, given the circumference formula, using Calculus but I suspect that's far too advanced for what you are going now.

You are probably just going to have to take these formulas as the Truth and go from there. (You might find the odd physical demonstration of these formulas, such as measuring the circumference and radius and finding a value for pi, that sort of thing.)

-Dan