vi + artha gives us vyartha.
In this case vi is used to mean without.
vyartha is waste – empty of meaning or purpose.
Contrast this with sva artha – svārtha which is advantageous to the individual,
para + artha parārtha which serves the purpose of others and
paramārtha which is the divine purpose or meaning.
Now try pra + artha = prārtha… towards purpose.
We use the word prārthana to mean prayer, it is when we seek help towards an artha.
(hindi people say matlabi – one with a hidden meaning/agenda to indicate a person who talks to you because he wants something.)
kŕtārtha is one who has achieved his purpose. kŕta + artha.
apa artha is apārtha the wrong meaning as when something is misunderstood.
Try different prefixes and see what words you can make.
….. and so on.