Question

A cuboid has a total surface area of 80m2 and its lateral surface area is

36m2. Find the area of the base. (Ans: 22m2) pls show the workout

Answer 1

The Area of the base is 22 m² .

Explanation:

Given as :

Total surface area of cuboid = TSA = 80 m²

Lateral surface area of cuboid = LSA = 36 m²

Let The Area of the base = x m²

The length of cuboid = L meters

The width of cuboid = W meters

The height of cuboid = H meters

Now, According to question

∵ Total surface area of cuboid = 2 × (Length × width + Length × height + height × width)

Or, TSA = 2 × (L × W + L × H + H × W)

Or, 2 × (L × W + L × H + H × W) = 80 m² ......1

Again

∵ Lateral surface area of cuboid = 2 × (Length × height + height × width)

Or, LSA = 2 × (L × H + H × W)

Or, 2 × (L × H + H × W) = 36 m² ..........2

Now, From eq 1 and eq 2

2 × (L × W) + 2 × (L × H + H × W) = 80 m²

Or, 2 × (Area of base) + 2 × (L × H + H × W) = 80 m²

Or, 2 × (x m²) + 36 m² = 80 m²

Or, 2 × (x m²) = 80 m² - 36 m²

Or, 2 x = 44 m²

∴ x =
`(44)/(2)`

i,e x = 22 m²

So, The Area of the base = x = 22 m²

Hence, The Area of the base is 22 m² . Answer