With a base and its perpendicular height, the area is ½ x base x height. If you only know the three sides, Heron's formula works: let s = (a + b + c) / 2, then area = √(s(s - a)(s - b)(s - c)).
Example: base 10 and height 6 give an area of 30. Sides 3, 4, 5 give s = 6 and area = √(6 x 3 x 2 x 1) = 6.
The two shorter sides must add up to more than the longest side. Sides 1, 2 and 5 cannot close into a triangle.
Only in a right triangle. Otherwise the height is the perpendicular distance from the base to the opposite corner.
See also: Pythagorean theorem calculator · circle calculator · square footage calculator