Final answer:
A contingency fee is a payment to a lawyer that is a percentage of the sum awarded to the client in a legal case.
Step-by-step explanation:
The type of fee that is billed as a percentage of an amount awarded to the client is known as a contingency fee. Lawyers typically use this fee arrangement in cases where they agree to represent a client with the understanding that their fees will be a percentage of the awarded amount if they win the case or settle out of court. This can be very common in personal injury cases, for example. If the lawyer does not win the case, they do not collect a fee, making it a risk for the lawyer but potentially advantageous for clients who might not be able to afford an attorney otherwise.