Regular hexagonal prism

Calculate the volume of a regular hexagonal prism whose body diagonals are 24cm and 25cm long.

Correct result:

V =  2636.7965 cm3

Solution:

u=24 cm v=25 cm  u1=2a  (u2/2)2+(a/2)2=a2 u22/4+a2/4=a2 u22/4+=3/4 a2  u2=3 a  h2+u12=v2 h2+u22=u2  h2+(2a)2=v2 h2+(3 a)2=u2 4a23a2=v2u2 a2=v2u2 a=v2u2=252242=7 cm  h=v24 a2=2524 72=429 cm20.7123 cm  S1=3 a24=3 72421.2176 cm2 S=6 S1=6 21.2176127.3057  V=S h=127.3057 20.7123=2636.7965 cm3



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