Question

the surface area of a cuboid is 95cm² and its lateral surface area is 63cm². find the area of its base​

Answer 1

The Area of the base is 16 cm² .

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) =
`(95)/(2)` ....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) =
`(63)/(2)` ......2

Putting value of eq 2 into eq 1

so, (l × b +
`(63)/(2)` ) =
`(95)/(2)`

Or, l × b =
`(95)/(2)` -
`(63)/(2)`

Or, l × b =
`(95 - 63)/(2)`

i.e l × b =
`(32)/(2)`

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