java.lang.IndexOutOfBoundsException with null arrayList

Hi my code works when tested with ArrayLists that contain objects but puts out the error java.lang.IndexOutOfBoundsException: Index: 0, Size: 0 when the arrayList is empty. What am I getting wrong.

ArrayList.get() is behaving exactly as documented.

Throws:
IndexOutOfBoundsException - if the index is out of range (index < 0 || index >= size())

There are no entries, so index 0 is out of bounds. If you want to return null if there are no rectangles, you should do that explicitly:

// Alternatively, if list.size() == 0
if (list.isEmpty()) {
    return null;
}

Note that a reference to an empty list is very different from a null reference, by the way. (Your title refers to a "null arrayList" - there's no such thing as a null object, but there can be a null reference... except there isn't in your case.)

This needs to be done before you otherwise call list.get(0) - and only once. (What's the point of calling it in the loop?) For example:

public Rectangle smallestArea() {
    if (list.isEmpty()) {
        return null;
    }
    Rectangle currentsmallestRectangle = list.get(0);
    // Note that you can go from 1, not 0...
    for (int i = 1; i < list.size(); i++) {
        Rectangle nextRectangle = list.get(i);
        if ((nextRectangle.getWidth() * nextRectangle.getHeight()) <
            (currentsmallestRectangle.getWidth() * 
             currentsmallestRectangle.getHeight())) {
            currentsmallestRectangle = nextRectangle;
        }
    }
    return currentSmallestRectangle;
}

Ideally, add an area() method to your Rectangle class, to make the loop simpler:

for (int i = 1; i < list.size(); i++) {
    Rectangle nextRectangle = list.get(i);
    if (nextRectangle.area() < currentSmallestRectangle.area()) {
        currentsmallestRectangle = nextRectangle;
    }
}