gaokao 2022 Q19

gaokao · China · national-A-arts 12 marks Vectors: Lines & Planes Volume of Pyramid/Tetrahedron Using Planes and Lines
Xiaoming designed a closed packaging box as shown in the figure: the bottom face $ABCD$ is a square with side length 2. Triangles $\triangle E A B , \triangle F B C , \triangle G C D , \triangle H D A$ are all equilateral triangles, and the planes containing them are perpendicular to the bottom face.
(1) Prove that $E F \parallel$ plane $A B C D$ ;
(2) Find the volume of the packaging box (disregarding the thickness of the material). 
Xiaoming designed a closed packaging box as shown in the figure: the bottom face $ABCD$ is a square with side length 2. Triangles $\triangle E A B , \triangle F B C , \triangle G C D , \triangle H D A$ are all equilateral triangles, and the planes containing them are perpendicular to the bottom face.\\
(1) Prove that $E F \parallel$ plane $A B C D$ ;\\
(2) Find the volume of the packaging box (disregarding the thickness of the material).
Paper Questions
Q1 Q5 Q6 Q7 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q18 Q19 Q20 Q22 Q23