[tex]A_b=l^2\\P_b=4*l\\A_l=P_b*h\\A_t=A_l+2*A_b\\V=A_b*h[/tex] formule piramidei parulatere regulate.
Înlocuim în formule:
a)
[tex]l=8, h=6 =>\\A_b=8^2=64\\P_b=4*8=32\\A_l=P_b*h=32*6=192\\A_t=A_l+2*A_b=192+2*64=192+128=230\\V=A_b*h=64*6=384[/tex]
b)
[tex]h=12, A_l=P_b*h=288 =>\\ P_b=288:12=24=>l=6\\A_b=6^2=36\\A_t=A_l+2*A_b=288+2*36=360\\V=A_b*h=36*12=432[/tex]
c)
[tex]h=10,V=A_b*h=2560=> A_b=2560:10=256=> A_b=l^2=>\\l=\sqrt{256}=16\\P_b=4*16=64\\A_l=P_b*h=64*10=640\\A_t=A_l+2*A_b=640+512=1152\\[/tex]
d)
[tex]h=12, A_l=P_b*h=576 =>\\ P_b=576:12=48=>l=12\\A_b=12^2=144\\A_t=A_l+2*A_b=576+2*144=864\\V=A_b*h=144*12=1728[/tex]
e)
[tex]A_t=1512 =>A_t=A_l+2*A_b=>2*A_b=1512-864=>A_b=324=>\\ A_b=l^2=> l=18\\ P_b=4*18=72A_l=864=>h=864:72=12\\V=A_b*h=324*12=3888[/tex]
f)
[tex]l=14,=>\\A_b=14^2=196\\P_b=4*14=56\\A_t=A_l+2*A_b=> A_l=1064-2*196=672\\\A_l=P_b*h=> h=772:56=12\\V=A_b*h=196*12=2352[/tex]
g)
[tex]l=10, h=8\sqrt{2} =>\\A_b=10^2=100\\P_b=4*10=40\\A_l=P_b*h=40*8\sqrt{2}=320\sqrt{2}\\A_t=A_l+2*A_b=320\sqrt{2}+200\\V=V=A_b*h}=100*8\sqrt{2}=800\sqrt{2}[/tex]
h)
[tex]l=18=>A_b=18^2=324\\P_b=4*18=72\\V=A_b*h=> h=4860:324=15\\A_l=P_b*h=72*15=1080\\A_t=A_l+2*A_b=1080+2*324=1728[/tex]
