Răspuns:
[tex]\boldsymbol {\red{A. \ 96 \ cm^2 }}[/tex]
Explicație pas cu pas:
Notăm VM apotema piramidei
<((VBC),(ABCD)) = <VMO
[tex]\sin VMO = \dfrac{VO}{VM}\Rightarrow \sin 60 = \dfrac{6}{VM}\Rightarrow \dfrac{ \sqrt{3} }{2} = \dfrac{6}{VM} \\ [/tex]
[tex]\Rightarrow VM = 4 \sqrt{3} \ cm[/tex]
[tex]\cos VMO = \dfrac{OM}{VM}\Rightarrow \cos 60 = \dfrac{OM}{4 \sqrt{3} }\Rightarrow \dfrac{1}{2} = \dfrac{OM}{4 \sqrt{3} } \\ [/tex]
[tex]\Rightarrow OM = 2 \sqrt{3} \ cm \Rightarrow AB = 4 \sqrt{3} \ cm \\ [/tex]
Aria laterală a piramidei este:
[tex]\mathcal {A}_{\ell} = \dfrac{\mathcal {P}_{b} \cdot a_{p}}{2} = \dfrac{4 \cdot AB \cdot VM}{2} = 2\cdot4 \sqrt{3}\cdot4 \sqrt{3} \\ [/tex]
[tex]= \bf 96 \ {cm}^{2} [/tex]
