Answer:
a) The surface area of a cuboid is given by the formula:
SA = 2lw + 2lh + 2wh
where l, w, and h are the length, width, and height of the cuboid, respectively.
In this case, we are given that:
h = xem
w = 2h = 2xem
l = 3h = 3xem
Substituting these values into the formula for the surface area of a cuboid, we get:
SA = 2(3xem)(2xem) + 2(3xem)(xem) + 2(2xem)(xem)
= 12xem^2
Therefore, the formula for the surface area of this cuboid is SA = 12xem^2.
b) Using the formula SA = 12xem^2, we can calculate the surface area of each cuboid and then add them to find the total surface area.
For cuboid A, x = 3, so the surface area is:
SA(A) = 12(3em)^2
= 108em^2
For cuboid B, x = 5, so the surface area is:
SA(B) = 12(5em)^2
= 300em^2
Therefore, the total surface area of the two cuboids is:
SA(A+B) = SA(A) + SA(B)
= 108em^2 + 300em^2
= 408em^2
So the total surface area of the two cuboids is 408em^2.