Pentagonal pyramid

Calculate the volume of a regular 5-side (pentaprism) pyramid ABCDEV; if |AB| = 7.7 cm and a plane ABV, ABC has angle 37 degrees.

Correct result:

V =  135.7761 cm

Solution:

a=7.7 u2=37 u1=360/5/2=36 tan(u1)=a/2/v1 v1=a/2/tanu1=a/2/tan36 =7.7/2/tan36 =7.7/2/0.726543=5.29907 S1=a v1/2=7.7 5.2991/220.4014 S5=5 S1=5 20.4014102.0071  tan(u2)=v/v1 v=v1 tanu2=v1 tan37 =5.29907039381 tan37 =5.29907039381 0.753554=3.99314 V=S5 v/3=102.0071 3.9931/3=135.7761 cm

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