Glass

How many glass are needed to produce glass with base regular 5-gon if one base triangle in the base is 4.2 square cm and the height is 10 cm?

Result

S =  195.685 cm2

Solution:

S1=5⋅ 4.2=21 h=10 S1=5/4 a2 tan⁡(54∘) a=4⋅ S1/5/tan⁡(54∘→rad)=4⋅ S1/5/tan⁡(54∘⋅ π180 )=4⋅ 21/5/tan⁡(54∘⋅ 3.1415926180 )=3.4937 o=5⋅ a=5⋅ 3.4937≐17.4685 S=S1+o⋅ h=21+17.4685⋅ 10≐195.6848=195.685 cm2S_{ 1 } = 5 \cdot \ 4.2 = 21 \ \\ h = 10 \ \\ S_{ 1 } = 5/4 \ a^2 \ \tan(54^\circ ) \ \\ a = \sqrt{ 4 \cdot \ S_{ 1 }/5 /\tan( 54 ^\circ \rightarrow rad) } = \sqrt{ 4 \cdot \ S_{ 1 }/5 /\tan( 54 ^\circ \cdot \ \dfrac{ \pi }{ 180 } \ ) } = \sqrt{ 4 \cdot \ 21/5 /\tan( 54 ^\circ \cdot \ \dfrac{ 3.1415926 }{ 180 } \ ) } = 3.4937 \ \\ o = 5 \cdot \ a = 5 \cdot \ 3.4937 \doteq 17.4685 \ \\ S = S_{ 1 } + o \cdot \ h = 21 + 17.4685 \cdot \ 10 \doteq 195.6848 = 195.685 \ cm^2

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