Given vertices A(1, 1), B(-3, 1), and C(-3, 3) of a rectangle ABCD, find the coordinates of vertex D and the lengths of sides AB and BC.

The three given vertices of the rectangle ABCD are $A(1, 1)$, $B(-3, 1)$, and $C(-3, 3)$. We need to find the coordinates of the fourth vertex, $D(x, y)$.

For a rectangle ABCD, opposite sides are parallel and equal in length. This means that the vector $\vec{AB}$ must be equal to the vector $\vec{DC}$.
First, calculate $\vec{AB}$:

Next, express $\vec{DC}$ in terms of $D(x, y)$:

Equating the components of $\vec{AB}$ and $\vec{DC}$:

So, the coordinates of the fourth vertex are $D(1, 3)$.
(Note: The hint "Coordinates of D are (3, 3)" is inconsistent with ABCD being a rectangle given the points A, B, and C. We proceed with the calculated coordinates for D.)

We can use the distance formula $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.
Length of side AB:

Length of side BC:

The area of a rectangle is given by the product of its length and width.

The coordinates of the fourth vertex are $\boxed{D(1, 3)}$ and the area of rectangle ABCD is $\boxed{8 \text{ square units}}$.