Octahedron

All walls of the regular octahedron are identical equilateral triangles. ABCDEF octahedron edges have a length d = 6 cm. Calculate the surface area and volume of this octahedron.

Correct answer:

S =  124.7077 cm²
V =  101.8234 cm³

Step-by-step explanation:

$$\begin{gathered} d=6\text{cm} \\ {S}_1=\sqrt{3}/4\cdot d^2=\sqrt{3}/4\cdot 6^2=9\sqrt{3}{\text{cm}}^2\doteq 15.5885{\text{cm}}^2 \\ S=8\cdot S_1=8\cdot 15.5885=72\sqrt{3}=124.7077{\text{cm}}^2 \end{gathered}$$

$V=\sqrt{2}/3\cdot d^3=\sqrt{2}/3\cdot 6^3=72\sqrt{2}=101.8234{\text{cm}}^3$

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