Question

1)Fie ABCDA'B'C'D' un paralelipiped dreptunghic cu AB-2radical3 cm,AA'-4RADICAL3 si At=24(2+radical 3 )cm patrativ:Aflati a) d[(A'AB),(D'DC)] B)V c) d d)m[<(D'DA),(D'DB)]

Answer 1

1)Fie ABCDA'B'C'D' un paralelipiped dreptunghic cu AB-2√3 cm,AA'-4√3 si At=24(2+√3 )cm²:Aflati
 a) d[(A'AB),(D'DC)]      AD
At= PxAA' +2Ab
At-2Ab= PxAA'
Ab=2√3xAD
48+24√3-2x2√3xAD=(2x2√3+2AD)4√3
48+24√3-4√3xAD=(4√3+2AD)4√3
48+24√3-4√3xAD=48+8√3AD
24√3=8√3AD+4√3AD
24√3=12√3AD
AD=2
 b)V  =Abxh= 2√3x2x4√3=48 cm³
c) diagonala bazei=√(2√3)²+2²=√(12+4)=√16=4
diagonala paralelipipedului =√(4)²+(4√3)²=√(16+48)=√64=8

d)m[<(D'DA),(D'DB)]
tg α =2√3/2=√3
α=60⁰