Hexagonal pyramid

Find the volume of a regular hexagonal pyramid, the base edge of which is 12 cm long and the side edge 20 cm.

Correct result:

V =  1995.323 cm3

Solution:

a=12 cm s=20 cm  S0=3/4⋅ a2=3/4⋅ 122≐36 3 cm2≐62.3538 cm2 S1=6⋅ S0=6⋅ 62.3538≐216 3 cm2≐374.123 cm2  s2=h2+a2 h=s2−a2=202−122=16 cm  V=13⋅ S1⋅ h=13⋅ 374.123⋅ 16=1995.323 cm3a=12 \ \text{cm} \ \\ s=20 \ \text{cm} \ \\ \ \\ S_{0}=\sqrt{ 3 }/4 \cdot \ a^2=\sqrt{ 3 }/4 \cdot \ 12^2 \doteq 36 \ \sqrt{ 3 } \ \text{cm}^2 \doteq 62.3538 \ \text{cm}^2 \ \\ S_{1}=6 \cdot \ S_{0}=6 \cdot \ 62.3538 \doteq 216 \ \sqrt{ 3 } \ \text{cm}^2 \doteq 374.123 \ \text{cm}^2 \ \\ \ \\ s^2=h^2+a^2 \ \\ h=\sqrt{ s^2-a^2 }=\sqrt{ 20^2-12^2 }=16 \ \text{cm} \ \\ \ \\ V=\dfrac{ 1 }{ 3 } \cdot \ S_{1} \cdot \ h=\dfrac{ 1 }{ 3 } \cdot \ 374.123 \cdot \ 16=1995.323 \ \text{cm}^3

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