Regular hexagonal prism

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

Correct answer:

V =  2636.7965 cm3

Step-by-step explanation:

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 4a2  3a2 = v2u2 a2 = v2u2 a=v2u2=252242=7 cm  h=v24 a2=2524 72=429 cm20.7123 cm  S1=43 a2=43 7221.2176 cm2 S=6 S1=6 21.2176127.3057  V=S h=127.3057 20.7123=2636.7965 cm3



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