[tex]V=\frac{A_b\times h}{3} \\\\A_b=\frac{3l^2\sqrt{3} }{2} \\\\A_l=\frac{P_b\times a_p}{2}[/tex]
[tex]A_b=\frac{3\times36\sqrt{3} }{2} =54\sqrt{3}cm^2[/tex]
[tex]54\sqrt{3} =\frac{54\sqrt{3} \times h}{3} \\\\h=3\ cm[/tex]
- Notam apotema bazei=[tex]a_b[/tex]
- Notam apotema piramidei=[tex]a_p[/tex]
[tex]a_b=\frac{l\sqrt{3} }{2} =3\sqrt{3} cm[/tex]
- Aplicam Pitagora in triunghiul format din inaltimea piramidei, apotema bazei si apotema piramidei, ipotenuza fiind apotema piramidei:
[tex]a_p^2=a_b^2+h^2[/tex]
[tex]a_p^2=27+9=36\\\\a_p=6\ cm[/tex]
[tex]P_b=6l=36cm\\A_l=\frac{36\times 6}{2} =108cm^2[/tex]
[tex]A_t=A_l+A_b\\\\A_t=108+54\sqrt{3}[/tex]
