Cost to Cover Prism

Calculate how much we will pay for the paper to cover the box in the shape of a three-sided prism with the base of a right-angled triangle; if the overhangs measure 12 cm and 1.6 decimeters, the hypotenuse measures 200 millimeters, the box is 27 centimeters high. We pay 0.26 euros for one square decimeter of paper.

Final Answer:

x =  3.87 Eur

Step-by-step explanation:

$$\begin{gathered} a=12\text{cm}\to \text{dm}=12:10\text{dm}=1.2\text{dm} \\ b=1.6\text{dm} \\ c=200\text{mm}\to \text{dm}=200:100\text{dm}=2\text{dm} \\ h=27\text{cm}\to \text{dm}=27:10\text{dm}=2.7\text{dm} \\ {S}_1=a\cdot b/2=1.2\cdot 1.6/2=\frac{24}{25}=0.96{\text{dm}}^2 \\ {S}_2=(a+b+c)\cdot h=(1.2+1.6+2)\cdot 2.7=\frac{324}{25}=12.96{\text{dm}}^2 \\ S=2\cdot S_1+S_2=2\cdot 0.96+12.96=\frac{372}{25}=14.88{\text{dm}}^2 \\ x=0.26\cdot S=0.26\cdot 14.88=3.87\text{Eur} \end{gathered}$$

Try another example