Hexagonal pyramid

Regular hexagonal pyramid has dimensions: length edge of the base a = 1.8 dm and the height of the pyramid = 2.4 dm. Calculate the surface area and volume of a pyramid.

Correct result:

S =  23.8716 dm²
V =  6.7342 dm³

Solution:

$$\begin{gathered} a=1.8\text{ dm } \\ v=2.4\text{ dm } \\ {h}_1=a\cdot \sqrt{3}\mathrm{/}2=1.8\cdot \sqrt{3}\mathrm{/}2\doteq 1.5588\text{ dm } \\ {h}_2=\sqrt{v^2+h_1^2}=\sqrt{2.4^2+1.5588^2}\doteq 2.8618\text{ dm } \\ {S}_1=a\cdot h_1\mathrm{/}2=1.8\cdot 1.5588\mathrm{/}2\doteq 1.403{\text{dm}}^2 \\ {S}_2=6\cdot S_1=6\cdot 1.403\doteq 8.4178{\text{dm}}^2 \\ {S}_3=a\cdot h_2\mathrm{/}2=1.8\cdot 2.8618\mathrm{/}2\doteq 2.5756{\text{dm}}^2 \\ S=S_2+6\cdot S_3=8.4178+6\cdot 2.5756=23.8716{\text{dm}}^2 \end{gathered}$$

$V={\displaystyle \frac{1}{3}}\cdot S_2\cdot v={\displaystyle \frac{1}{3}}\cdot 8.4178\cdot 2.4=6.7342{\text{dm}}^3$

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