Question

A cuboid has total surface area of 372 cm² and its lateral surface area is 180 cm², find the area of its base.

Answer 1

The area of the base of the cuboid is 96 cm².

• Given,

Total surface area of the cuboid = 372 cm²

Lateral surface area of the cuboid = 180 cm²

• Now, total surface area of a cuboid is given by 2 (lb + bh + lh) sqaure units, where,

l is the length of the cuboid,

b is the breadth of the cuboid,

and h is the height of the cuboid.

• Lateral surface area of a cuboid is the area of the lateral faces of the cuboid excluding its top and bottom faces.

• This implies that 2lb is not considered in the lateral surface area formula as the area of the top and bottom faces of a cuboid is 2lb.

• Therefore, the lateral surface area of a cuboid is given by 2 (bh + lh) square units.

• According to given,

2 ( lb + bh + lh) = 372 cm² -(i)

2 (bh + lh) = 180 cm² -(ii)

Or, bh + lh = 180 cm² / 2

Or, bh + lh = 90 cm² -(iii)

• Now, 2 (lb + 90 cm² ) = 372 cm², [from eq. (iii) ]

Or, lb + 90 cm² = 372 cm² / 2

Or, lb + 90 cm² = 186 cm²

Or, lb = 186 cm² - 90 cm²

Or, lb = 96 cm² -(iv)

• The base of a cuboid is a rectangle.

Area of a rectangle = length × breadth

Therefore, area of the base of the cuboid = lb = 96 cm² [ from eq. (iv) ]