Area of a triangle is one-half base times height. The height must be perpendicular to the base you chose. Base 10 and height 6 is 30. The full shape list is in area and volume.
Pick a base, then the height
Any side can be the base. The height is the perpendicular from the opposite vertex to that side, or to the line that side sits on. In a right triangle, the two legs can be base and height. Do not use a slant side as the height.
Trapezoids use a different average-of-the-bases formula, in area of a trapezoid. Equilateral shortcuts live with isosceles and equilateral triangles. Formulas as a set are in ACT Math formulas.
The bottom line
A = (1/2)bh. The h is perpendicular to the b you used.
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