Hexagonal pyramid

Calculate the surface area of a regular hexagonal pyramid with a base inscribed in a circle with a radius of 8 cm and a height of 20 cm.

Correct result:

S =  674.2611 cm2

Solution:

r=8 cm a=r=8=8 cm h=20 cm S1=3⋅ 3/2⋅ a2=3⋅ 3/2⋅ 82=96 3 cm2≐166.2769 cm2  a2=3/2⋅ a=3/2⋅ 8=4 3 cm≐6.9282 cm h2=a22+h2=6.92822+202=8 7 cm≐21.166 cm  S2=a⋅ h2/2=8⋅ 21.166/2=32 7 cm2≐84.664 cm2  S=S1+6⋅ S2=166.2769+6⋅ 84.664=674.2611 cm2

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