Height Is Not a Side

The height of a triangle is not one of its slanted sides. It is the straight drop from a corner to the line of the opposite side, meeting it at a right angle. Usually it falls inside the triangle, but it does not have to.

In this obtuse triangle the corner C hangs past the end of the base AB. The height from C drops down to the line of AB extended, at D, outside the triangle. The dashed extension BD is only there to show where the height lands. The area is still half the base AB times the height CD.

A slanted side is always longer than the height, so using it by mistake makes the area too big. In a right triangle, though, one leg stands at right angles to the other: there the height is a side.