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 answer:

V =  3016.1483 cm3
S =  1347.0581 cm2

Step-by-step explanation:

a=12.8 cm v=32.1 cm n=5  S1​=41​⋅ 5⋅ (5+2⋅ 5​)​⋅ a2=41​⋅ 5⋅ (5+2⋅ 5​)​⋅ 12.82≐281.883 cm2  V=31​⋅ S1​⋅ v=31​⋅ 281.883⋅ 32.1=3016.1483 cm3
S1​ = n ⋅  A T=S1​/n=281.883/5≐56.3766 cm2  T = 2a⋅ h1​​  h1​=a2⋅ T​=12.82⋅ 56.3766​≐8.8088 cm  h22​ = v2 + h12​  h2​=v2+h12​​=32.12+8.80882​≐33.2867 cm  S2​=2a⋅ h2​​=212.8⋅ 33.2867​≐213.035 cm2  S=S1​+n⋅ S2​=281.883+5⋅ 213.035=1347.0581 cm2

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Showing 2 comments:
Sebf
Perfect!
Thanks for demonstration
Really thanks
Sébastien

Sebf
I think we should see all the variables, I mean : a, v, n S1, S2 and all the things used to finally get the result S. On the scheme.
I understand the way you calculate on your savant literature. But I 'm sure i' m not the only one who would like to learn about this science visually.
For me it's OK. But I cannot share that.
Very sad while it is very clever.
Please explain how you get the result visually on the scheme.

Thanks by advance

Regards





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