Polygon Area and Type Identification

In the coordinate plane, consider a polygon with vertices A(1, 2), B(4, 6), C(7, 2), and D(4, -2). Determine the type of polygon formed by these vertices and its area.

Recall that the coordinates of the vertices can be used to analyze the polygon's shape and size. The formula for the area of a polygon given the coordinates of its vertices is:

$$ ext{Area} =\frac{1}{2} |x_1y_2 + x_2y_3 + x_3y_4 + x_4y_1 - (y_1x_2 + y_2x_3 + y_3x_4 + y_4x_1)| $$