本文从一道调研试题出发,通过三角形面积公式的不同形式的变化,把面积转化成函数、解析几何和不等式问题,笔者得到了试题的不同的解法,从中能感悟数学解题之美.题目(南京市、盐城市2017届高三年级第一次模拟考试)在△ABC中,A,B,C所对的边分别为a,b,c,若a~2+b~2+2c~2=8,则△ABC面积的最大值为____.试题结构平常,以三角形为背景,条件是三角形三边的关系式,所求的是三角形面积的最值.我 This article from a research questions, through the triangular area formula of different forms of change, the area into a function, analytic geometry and inequality problems, the author got a different solution to the questions, from which can understand the beauty of solving problems. , Yancheng 2017 third year high school first mock exam) △ ABC, A, B, C on the side of a, b, c, if a ~ 2 + b ~ 2 +2 c ~ 2 = 8, Then △ ABC area of ​​the maximum value of ____. Question structure is normal to the triangle as the background, the condition is the triangle of the three sides of the relationship, the triangle is the value of the area.