Tetrahedral pyramid

A regular tetrahedral pyramid is given. Base edge length a = 6.5 cm, side edge s = 7.5 cm. Calculate the volume and the area of its face (side area).

Correct result:

V =  83.4668 cm3
S =  87.8703 cm2

Solution:

a=6.5 cm s=7.5 cm  S1=a2=6.52=1694=42.25 cm2  u1=2⋅ a=2⋅ 6.5≐9.1924 cm  h=s2−(u1/2)2=7.52−(9.1924/2)2≐5.9266 cm  V=13⋅ S1⋅ h=13⋅ 42.25⋅ 5.9266=83.4668 cm3
h2=h2+(a/2)2=5.92662+(6.5/2)2≐6.7593 cm  S2=12⋅ a⋅ h2=12⋅ 6.5⋅ 6.7593≐21.9676 cm2  S=4⋅ S2=4⋅ 21.9676=87.8703 cm2

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