Hexagonal pyramid

Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length of 3 cm and a height of 5 cm.

Correct result:

V =  38.9711 cm3
S =  74.0951 cm2

Solution:

a=3 cm h=5 cm S1=3⋅ 3/2⋅ a2=3⋅ 3/2⋅ 32≐23.3827 cm2 V=S1⋅ h/3=23.3827⋅ 5/3=38.9711 cm3
a2=3/2⋅ a=3/2⋅ 3≐2.5981 cm h2=a22+h2=2.59812+52≐5.6347 cm S2=a⋅ h2/2=3⋅ 5.6347/2≐8.4521 cm2 S=S1+6⋅ S2=23.3827+6⋅ 8.4521=74.0951 cm2

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