Answer :
Note that the lateral surface area is the area of the faces of the solid, excluding the cross-sectional faces i.e. faces which are perpendicular to the longitudinal axis.
The lateral surface area of prism A is calculated as,
[tex]\begin{gathered} LSA_A=2(5\times3)+2(5\times3)_{} \\ LSA_A=30+30 \\ LSA_A=60 \end{gathered}[/tex]Similarly, the lateral surface area of prism A is calculated as,
[tex]\begin{gathered} LSA_B=2(3\times5)+2(5\times5)_{} \\ LSA_B=30+50 \\ LSA_B=80 \end{gathered}[/tex]Clearly, prisms A and B have different values of lateral surface area.
So option A is the correct statement.
The total surface area is the sum of all the faces of the solid.
Since we have already calculated the LSA i.e. sum of area of 4 faces of the prism, we can add the area of the two remaining cross sectional faces to get the total area.
The total cross section area of prism B is calculated as,
[tex]\begin{gathered} A_B=2(5\times3) \\ A_B=30 \end{gathered}[/tex]So the total surface area of prism B becomes,
[tex]\begin{gathered} TSA_B=LSA_B+A_B_{} \\ TSA_B=80+30 \\ TSA_B=110 \end{gathered}[/tex]The total surface area of prism B is 110 sq. cm.
So option B is also correct.
Note that we have already found that the lateral surface area of prism A is 60 sq. cm.
Therefore, option C is also correct.
The total cross section area of prism A is calculated as,
[tex]\begin{gathered} A_A=2(3\times5) \\ A_A=30 \end{gathered}[/tex]So the total surface area of prism A becomes,
[tex]\begin{gathered} TSA_A=LSA_A+A_A \\ TSA_A=60+30 \\ TSA_A=90 \end{gathered}[/tex]The total surface area of prism A is 90 sq. cm.
It is oberved that prism B has a larger surface area.
So, option D is also correct.
Hence, we can conclude that all the given statements are correct.