凸四边形的一个面积公式

• 作 者: 李明 单连峰
• 机 构: 中国医科大学数学教研室,
• 出 处: 数学通讯
• 发表日期: 2010年06期
• 关键词: 凸四边形 求解图 三条

1问题的提出众所周知,如果已知三角形的两边a1,a2及其夹角θ1(如图1),我们便有三角形面积的公式如下:S3=21a1a2sinθ1①图1图2将上述结论类比到凸四边形,我们便有如下问题:若已知凸四边形的三条边长依次为a1,a2和a3,且知道它们所夹的两个内角依次为θ1和θ2(如图2),则其面积S4?

As we all know, if we know the triangle a1, a2 and its included angle θ1 (Figure 1), we have the formula of the triangle area as follows: S3 = 21a1a2sinθ1① Figure 1 Figure 2 The above conclusion analogy to the convex quadrilateral, We have the following questions: If we know that the three sides of convex quadrilaterals are a1, a2 and a3 in turn, and know that the two internal angles they enclose are θ1 and θ2 (as shown in Figure 2), then the area S4?