Question

Can you help me with this, I’ve already completed the assignment but trying to go back and figure out what I missed and what I did wrong

Answer 1

OK

the base in this case is an hexagone

we can find the area of the base with the following formula

$A=\frac{3\sqrt{3}S^2}{2}$

where S represent the side of the hexagone

s=20

$A=\frac{3\sqrt{3}*20^2}{2}$$A=600\sqrt{3}=1039.23$

Perimiter is given by 6*S

P=6*20=120

h=22

Given the following formula for the hexagone

$A=\frac{p*a}{2}$

$600\sqrt{3}=\frac{120*a}{2}$

solving for a

$a=\frac{2*600\sqrt{3}}{120}=10\sqrt{3}=17.32$

applying pythagoras theorem

$l^2=a^2+h^2$$l^2=(10\sqrt{3})^2+22^2$$l=\sqrt{784}=28$

Lateral surface

$LS=\frac{p*l}{2}$$LS=\frac{120*28}{2}=1680$

Total surface

$TS=LS+A$$TS=1680+600\sqrt{3}$$TS=2719.23048$

Volume

$V=\frac{1}{3}A*h$$V=\frac{1}{3}600\sqrt{3}*22$$V=4400\sqrt{3}=7621.02$