Tetrahedral pyramid

Calculate the volume and surface area of a regular tetrahedral pyramid; its height is $b cm, and the length of the edges of the base is 6 cm.

Correct answer:

S =  196.1 cm²
V =  156 cm³

Step-by-step explanation:

$$\begin{gathered} a=6\text{cm} \\ h=13\text{cm} \\ s=\sqrt{h^2+(a/2{)}^2}=\sqrt{13^2+(6/2{)}^2}=\sqrt{178}\text{cm}\doteq 13.3417\text{cm} \\ {S}_1=a\cdot s/2=6\cdot 13.3417/2=3\sqrt{178}{\text{cm}}^2\doteq 40.025{\text{cm}}^2 \\ S=a^2+4\cdot S_1=6^2+4\cdot 40.025=196.1{\text{cm}}^2 \end{gathered}$$

$V=\frac{1}{3}\cdot a^2\cdot h=\frac{1}{3}\cdot 6^2\cdot 13=156{\text{cm}}^3$

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