inherit an interface, implement part of the methods, let a derived class implement the rest

Define the following C# interface:

public interface IShape
{
    int NumberOfLineSegments {get;}
    int Area {get;}
}

Next, I want to define several rectangle classes: Trapezoid, square,etc. All of these classes differ in their Area() property, but NumberOfLineSegments() always returns 4. Therefore, I would like an 'interim' class or interface, called Rectangle (or IRectangle), that looks something like:

public Rectangle : IShape
{
    public int NumberOfLineSegments{get{return 4;}}
}

I want Rectangle to implement only NumberOfLineSegment(), and leave it to its derived classes to implement the rest:

public Square : Rectangle 
{
    public int Area() {get{return length*height;}
}

However, since IShape is an interface, the Rectangle class must implement also Area(), which it knows not how to implement.. Thus I seem to be stuck, either with defining a 'dummy' Area() method for Rectangle, or not using inheritence at all.

Is there a way to circumvent this? I have read extensively through Richter's clr via c#, and in StackOverflow. Thanks in advance!