《数学通讯》2014年第5期刊登了程汉波老师的文章《四边形中位线的性质及其应用》,笔者阅读后深受启发,经过仔细推敲,得出平面内凸四边形的一组重要性质,现整理成文,与读者分享.性质1设平面内凸四边形ABCD的四边长分别为AB=a,BC=b,CD=c,DA=d,记其半周长为p=(a+b+c+d)/2,则四边形ABCD面积的最大值 In the 5th issue of Mathematical Newsletter 2014, Cheng Hanbo’s article “The Nature and Application of the Quadratic Median Line” was published. After reading this book, the author was inspired and after careful review, he obtained a set of important properties of the planar inward convex quadrilateral. Now collate the essay and share it with the reader. Property 1 Let the four sides of the in- plane convex quadrilateral ABCD be AB=a, BC=b, CD=c, and DA=d, and note that the semi-circumference is p=(a+b+c). +d)/2, the maximum value of quadric ABCD area