The shape in the question has two hexagonal faces,
The Area of each of the heaxagonal faces is
[tex]=42\text{ square units}[/tex]
The shape also has 6 rectangular faces with dimensions of
[tex]8.2\times4[/tex]
The area of a rectangle is gotten with the formula below
[tex]\text{Area}=l\times b[/tex]
By substituting the values, we will have
[tex]\begin{gathered} \text{Area}=l\times b \\ \text{Area}=8.2\times4 \\ \text{Area}=32.8\text{square units} \end{gathered}[/tex]
To calculate The total surface area of the shape, we will add up the areas of the hexagonal faces and the rectangular faces
[tex]\text{Surface area=}2\times(area\text{ of hexagonal faces)+ 6(area of rectangular faces)}[/tex]
By substituting the values, we will have
[tex]\begin{gathered} \text{Surface area=}2\times(area\text{ of hexagonal faces)+ 6(area of rectangular faces)} \\ \text{Surface area}=(2\times42)+(6\times32.8) \\ \text{Surface area}=84+196.8 \\ \text{Surface area}=280.8\text{ square units} \end{gathered}[/tex]
Hence,
The Surface Area is = 280.8 square units
