定理设D、B层分别在△ABC的边AC和AB上,BD与CE交于点P,AE:EB=m,AD:DC=χ,则 S_(AEFD)=(m·n)/(1+m+n)(1/(1+m)+(1+(1+n)S_(△ABC) (*) 证明略(留给读者练习) (*)式形式上对称易记,利用它可以简捷地求解一些面积问题。例1 如图2,平行四边形的面积是60,E、F分别是AB、BC的中点,AF分别和BD、BD交于G、H,则四边形BHGB的面积是__。(1991年江苏省初中竞赛题)。解在△ABD中,BH:HD=1:2,BE:EA=1,由(*)得 Theorem Let D and B be on the sides AC and AB of △ABC, BD and CE on point P, AE:EB=m, AD:DC=χ, then S_(AEFD)=(m·n)/( 1+m+n)(1/(1+m)+(1+(1+n)S_(△ABC) (*) Slightly (for readers to practice) (*) Symmetrical and easy to remember, use It can easily solve some area problems.Example 1 As shown in Figure 2, the area of ​​the parallelogram is 60, E and F are the midpoints of AB and BC respectively, and AF and BD and BD are intersected at G and H respectively, then the quadrilateral BHGB is The area is __.(1991 junior high school competition in Jiangsu Province). Solution in △ABD, BH:HD=1:2, BE:EA=1, obtained by (*)