Question

o prisma patrulatera regulata are dimensiunile proportionale cu 5 si 6 iar volumul egal cu 1200cm³.Aria laterala este egala cu?​

Answer 1

8.

Notam:

l=latura bazei

h=inaltimea prismei

{l,h} d.p {5,6}

$\frac{l}{5} =\frac{h}{6} =k$

l=5k

h=6k

V=1200cm³

$V=A_b\times h\\\\A_b=l^2=(5k)^2=25k^2\\\\1200=25k^2\times 6k\\\\1200=150k^3\\\\k^3=8\\\\k=2$

Daca k=2⇒ l=10 cm si h=12 cm

$A_l=P_b\times h\\\\P_b=4\times l=4\times 10=40\ cm\\\\A_l=40\times 12=480\ cm^2$