Answer:
The Area of the base is 22 m² .
Step-by-step 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 = [tex]\frac{44}{2}[/tex]
i,e x = 22 m²
So, The Area of the base = x = 22 m²
Hence, The Area of the base is 22 m² . Answer
