如图,某防洪指挥部发现长江边一处长600米,高10米,背水坡的坡角为45°的防洪大堤(横断面为梯形ABCD)

2025-05-10 15:42:06
推荐回答(1个)
回答1:

解:(1)分别过点E、D作EG⊥AB、DH⊥AB交AB于G、H.         
∵四边形ABCD是梯形,且AB∥CD,
∴DH平行等于EG.                                          
故四边形EGHD是矩形.                                      
∴ED=GH.                                                
在Rt△ADH中,
AH=DH=10(米).                         
在Rt△FGE中,
i=

1
3
=
EG
FG

∴FG=
3
EG=10
3
(米).                                       
∴AF=FG+GH-AH=10
3
+2-10=10
3
-8(米);

(2)∵S梯形ADEF=
(DE+AF)?DN
2
=
(2+10
3