Tetrahedral pyramid

Calculate the volume and surface of the regular tetrahedral pyramid if content area of the base is 20 cm2 and deviation angle of the side edges from the plane of the base is 60 degrees.

Correct result:

V =  36.51 cm3
S =  72.915 cm2

Solution:

S1=20 cm2 Φ=60  S1=a2 a=S1=20=2 5 cm4.4721 cm  u=2 a=2 4.4721=2 10 cm6.3246 cm  h=u2 tanΦ=u2 tan60 =6.32462 tan60 =6.32462 1.732051=5.47723  V=13 S1 h=13 20 5.4772=36.51 cm3
b=h2+(a/2)2=5.47722+(4.4721/2)2=35 cm5.9161 cm  S2=a b/2=4.4721 5.9161/2=5 7 cm213.2288 cm2  S=4 S2+S1=4 13.2288+20=72.915 cm2



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