Tetrahedron

Calculate the height and volume of a regular tetrahedron whose edge has a length of 13 cm.

Correct answer:

h =  10.61 cm
V =  244.11 cm3

Step-by-step explanation:

a=13 cm h12 = a2  (a/2)2  h1=36 a=36 1310.6145 cm  a2 = h2 + (2/3 h1)2  h=a2(2/3 h1)2=132(2/3 10.6145)210.6145   Verifying Solution:  h=h1=10.6145=10.61 cm
S1=2a h1=213 10.614568.994 cm2  V=31 S1 h=31 68.994 10.6145=92197244.1111 cm3   Verifying Solution:   V1=122 a3=122 133258.9189 cm3



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