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)214.2215 m  S2=a h22=5 14.2215235.5537 m2  S=S1+4 S2=25+4 35.5537=167.2146 m2



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