Question

How to find the height of a cuboid when given the surface area?

Answer 1

Hey there !

So let us take both the cases of Surface Area.

Lateral Surface Area is given:

Lateral Surface area of Cuboid = 2h ( l + b )

Let us assume the LSA to be x.

=> x = 2h ( l + b )

=> 2h = x / ( l + b )

=> h = x / 2 ( l + b )

So this is the formula that can be used for calculating while Lateral Surface Area is given.

Total Surface area = 2 ( lb + bh + hl )

Let us assume TSA to be y

=> y = 2 ( lb + bh + hl )

=> y = 2lb + 2bh + 2hl

=> y = 2lb + 2 h ( l + b )

=> y - 2lb = 2h ( l + b )

=> ( y - 2 lb ) / 2 ( l + b ) = h

=> h = ( y - 2 lb ) / 2 ( l + b )

This is the formula used when TSA is given.

Hope my answer helped !

Answer 2

Step-by-step explanation:

If Total Surface Area is given then ,

Height = Surface Area - 2 ( length × breadth ) / 2 ( length + breadth )

If Lateral Surface Area is given then ,

Height = Surface Area / 2 ( length + breadth )