For this problem, we are provided with all the faces of a solid figure, as well as its measurements. We need to determine the surface area of the image.
Let's draw the image and identify all the faces:
The total surface area will be equal to the sum of the area of each face. We have:
[tex]\begin{gathered} A_1=length*width=9.4\cdot5.6=52.64\text{ square cm}\\ \\ A_2=length*width=12.7\cdot9.4=119.38\text{ square cm}\\ \\ A_3=length*width=13.9\cdot9.4=130.66\text{ square cm}\\ \\ A_4=A_5=\frac{base*height}{2}=\frac{5.6\cdot12.7}{2}=35.56\text{ square cm} \end{gathered}[/tex]
Now we need to sum all the areas:
[tex]\begin{gathered} A=A_1+A_2+A_3+A_4+A_5 \\ A=52.64+119.38+130.66+35.56+35.56=373.8\text{ square cm} \end{gathered}[/tex]
The surface area is equal to 373.8 square centimeters.
