Answer:
The answer is "734.68".
Step-by-step explanation:
Given value:
edge length = 2 cm
height = [tex]\frac{\sqrt{2}}{2} \ cm[/tex]
volume = ?
[tex]\sqrt{2} = 1.41\\\\ \sqrt{3}= 1.73\\[/tex]
[tex]\ Area \ of \ hexagon \ = \frac{3 \sqrt{3}}{2} a^2\\\\\ Area = \frac{3 \sqrt{3}}{2} \times 2^2 \\\\\ Area = \frac{3 \sqrt{3}}{2} \times 2 \times 2 \\\\\ Area = 3 \sqrt{3} \times 2 \\\\\ Area = 6\sqrt{3} \\\\\ Area = 10.39 \\[/tex]
[tex]\ volume \ of \ octahedrons \ = \ Area \ of \ hexagon \times \ height \\\\[/tex]
[tex]= 10.39 \times \frac{\sqrt{2}}{2} \\\\= 734.68\\[/tex]
