In the figure (i) below, a cuboid is shown. The surface area of three faces are marked as x, y and z. In figure (ii), two such cuboids are stacked. Find the surface area of the new cuboid in figure (ii) in terms of x, y and z.

Given,

Let the dimensions of the cuboid be :

Length = l

Breadth = b

Height = h

From the figure (i) the three faces have areas:

x = length × height = lh

y = breadth × height = bh

z = length × breadth = lb

When two identical cuboids, are stacked the height is doubled (2h), length (l) and breadth (b) will remain same.

In (ii) figure,

Surface area of top face = length × breadth = lb = z

Surface area of right vertical face = length × height = 2lh = 2x

Surface area of left vertical face = breadth × height = 2bh = 2y

Total surface area = 2x + 2y + z.

Hence, surface area of new cuboid = 2x + 2y + z.