Salut!
35. Calculati aria laterala a unei prisme triunghiulare regulate cu aria bazei de [tex]\frac{25\sqrt3}{4}[/tex] si inaltimea=5.
[tex]A_{b}=\frac{l^2\sqrt3}{4}\\\\\frac{25\sqrt3}{4} =\frac{l^2\sqrt3}{4} \\\\100\sqrt3=4\sqrt3*l^2|:4\sqrt3\\\\25=l^2\\\\l=\sqrt{25}\\\\l=5[/tex]
[tex]A_{l}=P_{b}*h[/tex]
[tex]P_{b}[/tex]=3l=3*5=15
[tex]A_{l}=P_{b}*h\\\\A_{l}=15*5\\\\A_{l}=75[/tex]
36. Volumul unei prisme triunghiulare regulate este egal cu 144√3, iar inaltimea prismei este egala cu 12. Calculati aria totala a prismei.
[tex]V_{prismei}=A_{b}*h\\\\144\sqrt3=A_{b}*12|:12\\\\12\sqrt3=A_{b}[/tex]
[tex]A_{b}=\frac{l^2\sqrt3}{4}\\\\\frac{12\sqrt3}{1}=\frac{l^2\sqrt3}{4} \\\\48\sqrt3=l^2\sqrt3|:\sqrt3\\\\48=l^2\\\\l=\sqrt{48} \\\\l=4\sqrt3[/tex]
[tex]A_{t}=A_{l}+2*A_{b}[/tex]
[tex]A_{l}=P_{b}*h\\\\A_{l}=(4\sqrt3*3)*12\\\\A_{l}=12\sqrt3*12\\\\A_{l}=144\sqrt3[/tex]
[tex]A_{b}=\frac{l^2\sqrt3}{4} \\\\A_{b}=\frac{(4\sqrt3)^2*\sqrt3}{4} \\\\A_{b}=\frac{48\sqrt3}{4} \\\\A_{b}=12\sqrt3[/tex]
[tex]A_{t}=A_{l}+2*A_{b}\\\\A_{t}=144\sqrt3+2*12\sqrt3\\\\A_{t}=144\sqrt3+24\sqrt3\\\\A_{t}=164\sqrt3[/tex]
Succes!
