Answer:
The Area of the base is 16 cm² .
Step-by-step explanation:
Given as :
The surface area of the cuboid = x = 95 cm²
The lateral surface area of the cuboid = y = 63 cm²
Let The Area of the base = z cm²
Now, Let The length of cuboid = l cm
The breadth of cuboid = b cm
The height of cuboid = h cm
According to question
∵ The surface area of the cuboid = 2 ×(length × breadth + breadth × height + height × length)
Or, x = 2 ×(l × b + b × h + h × l)
Or, 95 = 2 ×(l × b + b × h + h × l)
Or, (l × b + b × h + h × l) = [tex]\dfrac{95}{2}[/tex] ....1
Similarly
∵lateral surface area of the cuboid = 2 ×(breadth × height + length × height)
Or, y = 2 ×(b × h + l × h)
Or, 2 ×(b × h + l × h) = 63
Or, (b × h + l × h) = [tex]\dfrac{63}{2}[/tex] ......2
Putting value of eq 2 into eq 1
so, (l × b + [tex]\dfrac{63}{2}[/tex] ) = [tex]\dfrac{95}{2}[/tex]
Or, l × b = [tex]\dfrac{95}{2}[/tex] - [tex]\dfrac{63}{2}[/tex]
Or, l × b = [tex]\dfrac{95 - 63}{2}[/tex]
i.e l × b = [tex]\dfrac{32}{2}[/tex]
so, l × b = 16
Now, Again
∵The Area of the base = ( length × breadth ) cm²
So, z = l × b
i.e z = 16 cm²
So, The Area of the base = z = 16 cm²
Hence,The Area of the base is 16 cm² . Answer
