The sum of the length and breadth of a cuboid is 4 cm. Length is three times of breadth. If the height of the cuboid is half of the sum of its length and breadth, then what is the total surface area of the cuboid?

22 cm²

We know that,

Total surface area of a cuboid = 2(lb + bh + lh)

We have,

Sum of length and breadth = 4 cm.

Length = 3 times of breadth.

Height = half of the sum of length and breadth.

= Let breadth = a.

= Length = 3a.

= Sum of length and breadth = a + 3a

 = 4a = 4

a = 1.

= Height = \(\frac{1}{2}\) ×  (Length + Breadth) = \(\frac{1}{2}\) × 4 = 2 cm.

= Total surface area = 2((3×1) + (1×2) + (2×3))

= 2(3 + 2 + 6) = 2 × 11 = 22 cm².