R=5 cm
diagonala fata=1 dm= 10 cm=d
Inaltime baza:
[tex]h_b=\frac{l\sqrt{3} }{2}[/tex]
[tex]R=\frac{2}{3}\times h_b\\\\ 5=\frac{2}{3}\times \frac{l\sqrt{3} }{2} \\\\5=\frac{l\sqrt{3} }{3} \\\\l=\frac{15}{\sqrt{3} } =5\sqrt{3}\ cm[/tex]
- Aflam inaltimea prismei din Pitagora:
Inaltimea prismei o notam cu h
Vom avea din Pitagora:
d²=h²+l²
100=h²+75
h²=25
h= 5 cm
[tex]A_l=P_b\times h[/tex]
[tex]P_b=3\times l=15\sqrt{3} \ cm[/tex]
[tex]A_l=15\sqrt{3} \times 5=75\sqrt{3} \ cm^2[/tex]
[tex]V=A_b\times h[/tex]
[tex]A_b=\frac{l^2\sqrt{3} }{4} =\frac{75\sqrt{3} }{4} \ cm^2[/tex]
[tex]V=\frac{75\sqrt{3} }{4}\times 5=\frac{375\sqrt{3} }{4} \ cm^3[/tex]
