a) Volumul prismei=20*20*10=4000 cm³
b)aria cutiei =20*20*2+20*10*4=800+800=1600 cm²
1600*110/100=1760 cm² folositi
c) daca O este mijlocum diagonalei EG, atunci O este centul patratului EFGH;
daca distanta CM este minima, atunci CM _|_ OB, sau CM este inaltime in ΔOBC
Mai intai calculam OB
in ΔOFB, <OFB=90
OF=HF/2= 20√2/2=10√2
OB²=OF²+FB²=200+100=300
OB=10√3
in Δisoscel OBC, OB=OC=10√3
ducem ON_|_BC, si avem BN=NC=10
ON²=OB²-BN²=300-100=200
ON=10√2
AriaΔOBC= ON*BC:2=CM*OB:2
Deci CM=ON*BC/OB=
=[tex] \frac{10 \sqrt{2}*20 }{10 \sqrt{3} } [/tex]=
=[tex] \frac{20 \sqrt{2} }{ \sqrt{3}} [/tex] |*[tex] \sqrt{3} [/tex]
CM=[tex] \frac{20 \sqrt{6} }{3} [/tex]
