Hexagonal prism 2

The regular hexagonal prism has a surface of 140 cm2 and height of 5 cm. Calculate its volume.

Correct result:

V =  20.1754 cm3

Solution:

h=5 S=140 S=2⋅ 6⋅ S1+6ah S=2⋅ 6⋅ a2⋅ 3/4+6ah 140=3⋅ 3⋅ a2+30a −5.19615242271a2−30a+140=0 D=b2−4ac=3809.84535672  a1=−8.8261406997≐−8.8261 a2=3.05263800781≐3.0526 a=a2=3.0526≐3.0526 S1=a2⋅ 3/4=3.05262⋅ 3/4≐4.0351 S2=6⋅ a⋅ h=6⋅ 3.0526⋅ 5≐91.5791 S3=2⋅ 6⋅ S1+S2=2⋅ 6⋅ 4.0351+91.5791=140 V=S1⋅ h=4.0351⋅ 5=20.1754 cm3

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