Tetrahedral pyramid

Calculate the surface S and the volume V of a regular tetrahedral pyramid with the base side a = 5 m and a body height of 14 m.

Correct result:

V =  116.6667 m3
S =  167.2146 m2

Solution:

a=5 m h=14 m  S1=a2=52=25 m2  V=13⋅ S1⋅ h=13⋅ 25⋅ 14=3503=116.6667 m3
h2=h2+(a/2)2=142+(5/2)2≐14.2215 m  S2=a⋅ h22=5⋅ 14.22152≐35.5537 m2  S=S1+4⋅ S2=25+4⋅ 35.5537=167.2146 m2

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