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To know how to find the surface area of a cuboidal shoe box, let us cut a cuboidal box of dimensions
l, b, and h and lay it flat as shown here.

l
b II
b l b

h
h I III IV V h

b l b
l VI b
l
The total surface area of a cuboid is equal to the area of all its six faces.

So, total surface area of a cuboid = area of face I + area of face II + area of face III + area of face
IV + area of face V + area of face VI

= h × l + b × l + b × h + l × h + b × h + l × b = 2(h × l + b × h + b × l)
= 2(lb + bh + hl)

where, l, b and h are the length, width, and height of the cuboid, respectively.
Thus, the total surface area of a cuboid = 2(lb + bh + hl) sq. units

Now, using this formula, we can find the area of cardboard needed to make a shoe box.
And then finally, the required cardboards for 1000 shoe boxes can be calculated.

Example 14: What will be the total surface area of the cuboid shown
in the given figure? 3 cm

Solution: Here, length = 6 cm, breadth = 4 cm, and height = 3 cm. 4 cm
6 cm
\ Total surface area of the cuboid = 2(lb + bh + hl)
2
= 2(6 × 4 + 4 × 3 + 3 × 6) cm = 2(24 + 12 + 18) cm 2
= 2(54) cm = 108 cm 2
2
2
Thus, the surface area of the cuboid is 108 cm .
Lateral Surface Area

If we do not include the area of the top and bottom faces, then the area of its walls are called the
lateral surface area of a cuboid.
Top
Look at the adjoining figure, the highlighted area makes the lateral
surface area of the cuboid.

Lateral surface area of a cuboid = Area of four walls
h
= h × l + b × h + l × h + b × h
l b
= 2(h × l + b × h)
Base
= 2h(l + b) sq. units.
\ Lateral surface area of a cuboid = 2h(l + b) sq. units

243 Mensuration