We have right angled triangle ABC with the right angle at vertex A. The hypotenuse length is "a" units, and the leg AC has the length x (given). (a) Apply Pythagorean theorem : | BC | == . it is the expression you are looking for. (b) Area is half of the product of leg lengths A = . (c) The domain of this function is 0 < x < 12. The endpoints 0 and 12 are not included to the domain, since otherwise the triangle becomes degenerated.