It depends upon what you are calling height and what the thing is, what the area is, that is being measured.
If you have a three dimensional shape and are measuring the area of the base which has dimensions length and width, then the height is irrelevant.
If you have a three dimensional shape and are measuring the area of the back then the area will be calculated as width times height and you need to consider the height
If you have a room and are considering how much paint you need to buy to paint the walls, then you are calculating the surface area of the walls and will need to consider the height as you will have 2 walls length × height and 2 walls width × height.
If you are considering the surface area of a cuboid, then the height will also need to be considered as you will have 2 faces each of width × length, length × height, height × width.
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Square metres are the area of a flat plain figure (length x width of a floor). Height is only considered if calculating the volume in cubic metres of a 3D object (Length x width x height of a box or room, for example).
The answer depends on the surface whose area you wish to calculate. If a wall, then yes; if a floor, then no.