Triangular pyramid

It is given perpendicular regular triangular pyramid: base side a = 5 cm, height v = 8 cm, volume V = 28.8 cm3. What is it content (surface area)?

Correct result:

S =  71.79 cm2


a=5 cm h=8 cm V=28.8 cm3  h1=a2(a/2)2=52(5/2)24.3301 cm S1=a h12=5 4.3301210.8253 cm2    h22=h2+(h1/3)2 h2=h2+(h1/3)2=82+(4.3301/3)28.1292 cm  S2=a h22=5 8.1292220.3229 cm2  S=S1+3 S2=10.8253+3 20.322971.7941=71.79 cm2   Verifying Solution:  V2=13 S1 h=13 10.8253 828.8675 cm3 V2=V

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