Tetrahedral pyramid

Determine the surface of a regular tetrahedral pyramid when its volume is V = 120 and the angle of the sidewall with the base plane is α = 42° 30´.

Correct result:

S =  200.6434

Solution:

V=120 A=42+3060=852=42.5 A1=A rad=A π180 =42.5 3.1415926180 =0.74176=17π/72  tanA=h/(a/2)  h=a/2 tanA V=13a2 h V=16a3 tanA  a=6 V/tan(A1)3=6 120/tan(0.7418)39.2277  h=a/2 tan(A1)=9.2277/2 tan(0.7418)4.2278 sinA1=h:w  w=h/sin(A1)=4.2278/sin(0.7418)6.258  S1=a w/2=9.2277 6.258/228.8733  S=a2+4 S1=9.22772+4 28.8733=200.6434



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