Paper box

Calculate how much we'll pay for a three-side shaped prism box with a triangular base, and if it measures 12cm and 1.6dm, the hypotenuse measures 200mm. The box is 34cm high. We pay 0,13 € per square meter of paper.

Result

x =  2.37 Eur

Solution:

a=12 cm=12/10 dm=1.2 dm b=1.6 dm c=200 mm=200/100 dm=2 dm  h=34 cm=34/10 dm=3.4 dm  S1=a⋅ b/2=1.2⋅ 1.6/2=2425=0.96 dm2 S2=(a+b+c)⋅ h=(1.2+1.6+2)⋅ 3.4=40825=16.32 dm2  S=2⋅ S1+S2=2⋅ 0.96+16.32=45625=18.24 dm2  x=0.13⋅ S=0.13⋅ 18.24=1482625=2.3712=2.37 Eura=12 \ cm=12 / 10 \ dm=1.2 \ dm \ \\ b=1.6 \ \text{dm} \ \\ c=200 \ mm=200 / 100 \ dm=2 \ dm \ \\ \ \\ h=34 \ cm=34 / 10 \ dm=3.4 \ dm \ \\ \ \\ S_{1}=a \cdot \ b / 2=1.2 \cdot \ 1.6 / 2=\dfrac{ 24 }{ 25 }=0.96 \ \text{dm}^2 \ \\ S_{2}=(a+b+c) \cdot \ h=(1.2+1.6+2) \cdot \ 3.4=\dfrac{ 408 }{ 25 }=16.32 \ \text{dm}^2 \ \\ \ \\ S=2 \cdot \ S_{1} + S_{2}=2 \cdot \ 0.96 + 16.32=\dfrac{ 456 }{ 25 }=18.24 \ \text{dm}^2 \ \\ \ \\ x=0.13 \cdot \ S=0.13 \cdot \ 18.24=\dfrac{ 1482 }{ 625 }=2.3712=2.37 \ \text{Eur}

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