Wooden prism painting

The kit contains wooden prisms of various shapes. One is 4-sided with the base of a rectangular trapezoid (base measures 15cm and 27cm), arms 16cm and 20cm. The other was a 3-sided prism with base dimensions a=20cm, b=18cm, vb=30cm. Both prisms had a height of 10cm paint.

Final Answer:

S =  25.72 dm²

Step-by-step explanation:

$$\begin{gathered} a=15\text{cm} \\ c=27\text{cm} \\ b=16\text{cm} \\ d=20\text{cm} \\ h=10\text{cm} \\ {z}_1=20\text{cm} \\ {z}_2=18\text{cm} \\ {h}_2=30\text{cm} \\ {S}_1=2\cdot \frac{a+c}{2}\cdot b+(a+b+c+d)\cdot h=2\cdot \frac{15+27}{2}\cdot 16+(15+16+27+20)\cdot 10=1452{\text{cm}}^2 \\ {S}_2=2\cdot \frac{z_2\cdot h_2}{2}+h\cdot (z_1+z_2+z_1)=2\cdot \frac{18\cdot 30}{2}+10\cdot (20+18+20)=1120{\text{cm}}^2 \\ {S}_3=S_1+S_2=1452+1120=2572{\text{cm}}^2 \\ S=S_3\to {\text{dm}}^2=S_3:100{\text{dm}}^2=2572:100{\text{dm}}^2=25.72{\text{dm}}^2=\frac{643}{25}{\text{dm}}^2=25.72{\text{dm}}^2 \end{gathered}$$

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