平行四边形中求阴影面积
来源:学生作业帮 编辑:百度作业网作业帮 分类:数学作业 时间:2024/08/13 18:57:03
平行四边形中求阴影面积
如图啦,
剩下的就是麻烦大家了.
![](http://img.wesiedu.com/upload/f/1f/f1f768e9a416c3e9e072ae194355724c.jpg)
如图啦,
剩下的就是麻烦大家了.
![](http://img.wesiedu.com/upload/f/1f/f1f768e9a416c3e9e072ae194355724c.jpg)
![平行四边形中求阴影面积](/uploads/image/z/2575858-58-8.jpg?t=%E5%B9%B3%E8%A1%8C%E5%9B%9B%E8%BE%B9%E5%BD%A2%E4%B8%AD%E6%B1%82%E9%98%B4%E5%BD%B1%E9%9D%A2%E7%A7%AF)
延长BE,CD交于M
MD/AB=1/3
MF/AB=MD/AB+DF/AB=1/3+2/9=5/9
S△EDM/S△AEB=(1/3)^2=1/9
S△AEB/SABCD=1/2*3/(3+1)=3/8
S△EDM/SABCD=1/9*3/8=1/24
S△GFM/S△AGB=(5/9)^2=25/81
S△AGB/SABCD=1/2*9/(5+9)=9/28
S△GFM/SABCD=25/81*9/28=25/252
S阴影/SABCD=S△GFM/SABCD-S△EDM/SABCD
=25/252-1/24=29/504
S阴影=29/504*256=32*29/63=928/63
应该没有算错!
MD/AB=1/3
MF/AB=MD/AB+DF/AB=1/3+2/9=5/9
S△EDM/S△AEB=(1/3)^2=1/9
S△AEB/SABCD=1/2*3/(3+1)=3/8
S△EDM/SABCD=1/9*3/8=1/24
S△GFM/S△AGB=(5/9)^2=25/81
S△AGB/SABCD=1/2*9/(5+9)=9/28
S△GFM/SABCD=25/81*9/28=25/252
S阴影/SABCD=S△GFM/SABCD-S△EDM/SABCD
=25/252-1/24=29/504
S阴影=29/504*256=32*29/63=928/63
应该没有算错!