To calculate the surface area of the object on the picture, you have to calculate the area of each face and then add them together.
The figure has 6 faces, each face is quadrilateral and the opposite faces are equal, which means that the shape has 3 pairs of congruent faces.
1. The top and bottom faces are rectangular, with length l=11cm and width w=16cm.
To determine the area of these faces you have to multiply the length by the width:
[tex]A=l\cdot w[/tex]
Since both faces are equal, you have to multiply it by 2:
[tex]\begin{gathered} 2A=2(lw) \\ 2A=2(11\cdot16) \\ 2A=2\cdot176 \\ 2A=352\operatorname{cm}^2 \end{gathered}[/tex]
2. The front and back faces are parallelograms with base b=11cm and height h=6.7cm.
To determine the area of a parallelogram you have to multiply its base by its height:
[tex]A=b\cdot h[/tex]
As before, both faces are equal, to determine the area of both, multiply the area by 2:
[tex]\begin{gathered} 2A=2(bh) \\ 2A=2(11\cdot6.7) \\ 2A=2\cdot73.7 \\ 2A=147.4\operatorname{cm}^2 \end{gathered}[/tex]
3. The remaining faces are rectangular with width w=16cm and height h=7cm.
To determine the area you have to multiply the width by the height:
[tex]A=w\cdot h[/tex]
Once again, since there are two equal faces, you have to multiply the area by 2:
[tex]\begin{gathered} 2A=2(wh) \\ 2A=2(16\cdot7) \\ 2A=2\cdot112 \\ 2A=224\operatorname{cm}^2 \end{gathered}[/tex]
Now that the area of all 6 faces of the shape is determined, you have to add them:
[tex]\begin{gathered} SA=352+147.4+224 \\ SA=723.4\operatorname{cm}^2 \end{gathered}[/tex]
The surface area of the shape is 723.4cm²
