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What is the area of a triangle if the base is 12 inches and the height is 18 inches?

  • geometry -

    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.

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