Quadrangular pyramid

The regular quadrangular pyramid has a base length of 6 cm and a side edge length of 9 centimeters. Calculate its volume and surface area.

Correct result:

V =  95.247 cm3
S =  137.8234 cm2

Solution:

a=6 cm s=9 cm  S1=a2=62=36 cm2  u=2⋅ a=2⋅ 6=6 2 cm≐8.4853 cm  h=s2−(u/2)2=92−(8.4853/2)2=3 7 cm≐7.9373 cm  V=13⋅ S1⋅ h=13⋅ 36⋅ 7.9373=36 7=95.247 cm3
h2=s2−(a/2)2=92−(6/2)2=6 2 cm≐8.4853 cm  S2=a⋅ h2/2=6⋅ 8.4853/2=18 2 cm2≐25.4558 cm2  S=S1+4⋅ S2=36+4⋅ 25.4558=137.8234 cm2

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