Question

ABCDA'B'C'D'-paralelipiped dreptunghic
AB=8
CC'=6
C'E=2√22
E e(AB) si [AE] congruent [EB]
a)A totala si Volum=?
b)distanta(A',BC')

Answer 1

Răspuns:

Explicație pas cu pas:

AB=8, AE=EB, deci EB=4. C'C=6,  C'E=2√22

C'C⊥(ABC), ⇒C'C⊥CE, deci ΔC'CE dreptunghic. ⇒CE²=C'E²-C'C²=(2√22)²-6²=4·22-36=4·(22-9)=4·13,

Din ΔBCE, dereptunghic in B, ⇒BC²=CE²-BE²=4·13-4²=4·(13-4)=4·9. Deci BC=√(4·9)=2·3=6.

Aria(t)=Aria(l)+2·Aria(b).

Aria(l)=P(b)·h=2·(AB+BC)·C'C=2·(8+6)·6=2·14·6=28·6=168

Aria(b)=AB·BC=8·6=48

Deci Aria(t)=168+2·48=168+96=264.

Volum=Aria(b)·h=48·C'C=48·6=288

d(A',BC')=d(A,BC')=AB=8