Question

Fie paralelipipedul drept.ABCDA'B'C'D'.Stiind ca AB=2radical5,BC=3radical2,AA'=4radical10,calculati aria totala,volumul,diagonala.

Answer 1

AB=L
BC=l
AA'=h
Volum=L*l*h=$2 \sqrt{5} *3 \sqrt{2} *4 \sqrt{10} =24 \sqrt{100} =240$
Aria=2(L*l+L*h+l*h)=2($2 \sqrt{5} *3 \sqrt{2} +2 \sqrt{5} *4 \sqrt{10} +3 \sqrt{2} +4 \sqrt{10} )$=2($6 \sqrt{10} +6 \sqrt{50} +8 \sqrt{20})$=$12 \sqrt{10} +12 \sqrt{50} +16 \sqrt{20}$
diagonala=$\sqrt{20+18+160} =\sqrt{198}$