How Do You Calculate the Moment of Inertia for a Rectangular Sheet?

[HeartOfLions]

Homework Statement

A thin, rectangular sheet of metal has mass M and sides of length a and b. Find the moment of inertia of this sheet about an axis that lies in the plane of the plate, passes through the center of the plate, and is parallel to the side with length b.
Express your answer in terms of given quantities.

Find the moment of inertia of the plate for an axis that lies in the plane of the plate, passes through the center of the plate, and is perpendicular to the axis in part A.
Express your answer in terms of given quantities.

Homework Equations

I = integral of (r² dm)
I = m*r²
I = c*M*L²

The Attempt at a Solution

I don't really understand this questions concept of inertia, any help would be appreciated. The textbook is not helpful with this specific question. Could someone point me to a website or examples to help me understand this?

 

[rock.freak667]

Let the area density be denoted by σ i.e. σ=M/A

$$\int r^2 dm \equiv \int \sigma r^2 dA$$So let's consider a small rectangular element of width dx and length dy. The distance of of this element from any corner is r (so what is r in terms of x and y?)What is the area of this element dA?