Pentagonal pyramid

Find the volume and surface of a regular pentagonal pyramid with a base edge a = 12.8 cm and a height v = 32.1 cm.

Correct result:

V =  3016.1483 cm3
S =  1347.0581 cm2

Solution:

a=12.8 cm v=32.1 cm n=5  S1=14⋅ 5⋅ (5+2⋅ 5)⋅ a2=14⋅ 5⋅ (5+2⋅ 5)⋅ 12.82≐281.883 cm2  V=13⋅ S1⋅ v=13⋅ 281.883⋅ 32.1=3016.1483 cm3
S1=n⋅ a⋅ h12  h1=2⋅ S1/n/a=2⋅ 281.883/5/12.8≐8.8088 cm  h2=v2+h12=32.12+8.80882≐33.2867 cm  S2=a⋅ h22=12.8⋅ 33.28672≐213.035 cm2  S=S1+n⋅ S2=281.883+5⋅ 213.035=1347.0581 cm2

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