A cuboid has a total surface area of 80 m² and the lateral surface area of 50 m²; the area of its base is :

1. 30 m²

2. 60 m²

3. 15 m²

4. 10 m²

The total surface area of the cuboid = 80 m²

The lateral surface area of the cuboid = 50 m²

As we know, the total surface area of the cuboid = 2(l x b + b x h + h x l)

⇒ 80 = 2(l x b + b x h + h x l)

⇒ 80 = 2(l x b) + 2(b x h) + 2(h x l) …………..(1)

The lateral surface area of the cuboid = 2(l + b)h = 2(l x h + b x h)

⇒ 50 = 2(l x h) + 2(b x h) …………..(2)

And, area of base = l x b

Putting the value of 2(l x h) + 2(b x h) from equation (2) in equation (1), we get

⇒ 80 = 2(l x b) + 50

⇒ 2(l x b) = 80 - 50

⇒ 2(l x b) = 30

⇒ l x b = $\dfrac{30}{2}$

⇒ l x b = 15 m²

Hence, option 3 is the correct option.