Question

一个多面体的直观图和三视图如图所示，其中M、G分别是AB、DF的中点。

（1）       在AD上（含A、D端点）确定一点P，使得GP//平面FMC；

（2）       一只苍蝇在几何体ADF-BCE内自由飞翔，求它飞入几何体F-AMCD内的概率。

                                                                         

                                                                          

                                                                             

                                                                       

                                                                        

                                                                        

                                                                         

                                                                         

Answer 1

(Ⅰ) 略(Ⅱ)

解析:

：由三视图可得直观图为直三棱柱且底面ADF中AD⊥DF,DF=AD=DC

(1)点P在A点处  证明：取DC中点S，连接AS、GS、GA

∵G是DF的中点，GS//FC，AS//CM

∴面GSA//面FMC，而GA面GSA…………9分

（2）   所以概率为 …………12分