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众所周知,若三角形ABC的三边长分别为a、b、c,则有面积公式:(1)S=1/2ah(h为BC边上的高);(2)S=1/2absin C;(3)S=(p(p-a)(p-b)(p-c))~(1/2)(p=(a+b+c)/2).应用时,根据三角形不同条件或不同的思路选取相对应的面积公式.而在解析几何中,求三角形面积的问题十分活跃,通常解答方法是求弦长与高,代入S=1/2ah进行求解,计算量较大,易发生错误.若给出三角形面积向量公式,
It is well-known that if the triangle sides of a triangle ABC are a, b, c, respectively, then there is an area formula: (1) S = 1/2ah (h is the height on the edge of BC); (2) S = 1/2absin C; (3) S = (p (pa) (pb) (pc)) ~ (1/2) (p = (a + b + c) / 2) When applying, according to different conditions of the triangle or different ideas The corresponding area formula.And in analytic geometry, the problem of seeking triangle area is very active, the usual solution is to ask chord length and height, into the S = 1 / 2ah solution, the calculation is large, prone to error.If given Triangle area vector formula,