Work done can be measured as area of force and displacement graph. We can take displacement on x axis and force on y axis while drawing the graph. The nature and look of the graph depends on how force is changing with displacement.
The area covered under the graph can be identified using the mathematical tools basing on the shape of the graph.If the shape is triangle, work done is half of base and height as it is the formula for the area of triangle. If the shape is a rectangle, area of the graph is nothing but product of length and breadth and that gives the work done in that case.
If the graph is in random order, we can divide that graph into many parts and we can find the area of each part. The total work done is nothing but sum of all the areas of the graph. This can be measured much easily using mathematical integration method.
Work is said to be done only when applied force is able to produce displacement. If displacement is taken on x axis and it is equal to zero, the graph will be a straight line parallel to Y axis and hence area covered in the graph is equal to zero. Hence work done in this case is also zero. If there is no displacement generated by the applied force, work done by that force is equal to zero.
Graphical representation is done in the following video as shown below.
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