Question 972120
See if you have a side or an angle. 

If the perpendicular comes to a side, and you have the measure of the side's length, you can get the area.

A perpendicular with no side lengths and no angle measurements is insufficient to get a triangle's area.  It could be anything.  If there is a side and an angle, the Law of Cosines may apply.  If there is a base, you can obtain the area directly.

The perpendicular forms a right angle with a side.  Having that, there may be a use for the Pythagorean theorem, but again, you need side lengths with a scalene triangle, or you need angle sizes.