Question

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

Answer 1

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) = $\dfrac{95}{2}$          ....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) = $\dfrac{63}{2}$              ......2

Putting value of eq 2 into eq 1

so,  (l × b +  $\dfrac{63}{2}$ ) = $\dfrac{95}{2}$    

Or, l × b = $\dfrac{95}{2}$ - $\dfrac{63}{2}$    

Or,  l × b = $\dfrac{95 - 63}{2}$

i.e l × b = $\dfrac{32}{2}$

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