Tetrahedral pyramid

It is given a regular tetrahedral pyramid with base edge 6 cm and the height of the pyramid 10 cm. Calculate the length of its side edges.

Correct result:

s =  10.863 cm

Solution:

a=6 cm h=10 cm  u=a⋅ 2=6⋅ 2≐6 2≐8.4853  s=h2+(u/2)2=102+(8.4853/2)2=118=10.863 cma=6 \ \text{cm} \ \\ h=10 \ \text{cm} \ \\ \ \\ u=a \cdot \ \sqrt{ 2 }=6 \cdot \ \sqrt{ 2 } \doteq 6 \ \sqrt{ 2 } \doteq 8.4853 \ \\ \ \\ s=\sqrt{ h^2+(u/2)^2 }=\sqrt{ 10^2+(8.4853/2)^2 }=\sqrt{ 118 }=10.863 \ \text{cm}

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