posted by Phil .
What is the area of a triangle if the base is 12 inches and the height is 18 inches?
With no knowledge of the trigonometry of triangles, argue it like this. The question wouldn't have been asked if there wasn't a unique answer, so the answer must be the same regardless of whereabouts above the base the apex is - including the special case in which it's directly above one of the ends of the base. That would make the base and vertical two sides of a rectangle of lengths 12 and 18 inches respectively. That would make the area of the rectangle 12x18=216 square inches, and the triangle must be half of this, which is 108 square inches. Now do it properly: the rule is that the area of a triangle is half the base times the height, which is 12x18/2 = 12x9 = 108 square inches.