Regular hexagonal prism

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

Final 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 = v2−u2 a2 = v2−u2 a=v2−u2​=252−242​=7 cm  h=v2−4⋅ a2​=252−4⋅ 72​=429​ cm≐20.7123 cm  S1​=43​⋅ a2​=43​⋅ 72​≐21.2176 cm2 S=6⋅ S1​=6⋅ 21.2176≐127.3057  V=S⋅ h=127.3057⋅ 20.7123=2636.7965 cm3

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