OK
the base in this case is an hexagone
we can find the area of the base with the following formula
[tex]A=\frac{3\sqrt{3}S^2}{2}[/tex]
where S represent the side of the hexagone
s=20
[tex]A=\frac{3\sqrt{3}*20^2}{2}[/tex][tex]A=600\sqrt{3}=1039.23[/tex]
Perimiter is given by 6*S
P=6*20=120
h=22
Given the following formula for the hexagone
[tex]A=\frac{p*a}{2}[/tex]
[tex]600\sqrt{3}=\frac{120*a}{2}[/tex]
solving for a
[tex]a=\frac{2*600\sqrt{3}}{120}=10\sqrt{3}=17.32[/tex]
applying pythagoras theorem
[tex]l^2=a^2+h^2[/tex][tex]l^2=(10\sqrt{3})^2+22^2[/tex][tex]l=\sqrt{784}=28[/tex]
Lateral surface
[tex]LS=\frac{p*l}{2}[/tex][tex]LS=\frac{120*28}{2}=1680[/tex]
Total surface
[tex]TS=LS+A[/tex][tex]TS=1680+600\sqrt{3}[/tex][tex]TS=2719.23048[/tex]
Volume
[tex]V=\frac{1}{3}A*h[/tex][tex]V=\frac{1}{3}600\sqrt{3}*22[/tex][tex]V=4400\sqrt{3}=7621.02[/tex]
