Tetrahedron

Calculate height and volume of a regular tetrahedron whose edge has a length 6 cm.

Correct answer:

h =  4.9 cm
V =  24 cm3

Step-by-step explanation:

a=6 cm h12=a2(a/2)2  h1=63 a=63 6=2 6 cm4.899 cm  a2=h2+(2/3 h1)2  h=a2(2/3 h1)2=62(2/3 4.899)2=2 64.899   Verifying Solution:  h=h1=4.899=2 6=4.9 cm
S1=a h12=6 4.8992=6 6 cm214.6969 cm2  V=13 S1 h=13 14.6969 4.899=24=24 cm3   Verifying Solution:   V1=212 a3=212 63=18 2 cm325.4558 cm3



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