A cuboid, on its base, is a 3-d shape and four of its edges are vertical.
A shape is not a sufficiently specific term. It can have two dimensions: length and breadth, or 3 dimensions (L, B and depth). Sometimes "width" is used instead. But in mathematics there can be shapes in 4 or more dimensions.
square
You have given 3 dimensions and not the shape. For area you generally need two dimensions, like for a rectangle. The area of this is Length by width.
A cube is one of them.
A rectangle is a 2-dimensional shape. Its equivalent in 3-dimensions is a cuboid. The equivalent of a cuboid in 4 or more spatial dimensions is a hyper-cuboid.
If one dimension of a 3-dimensional shape is doubled, the volume increases by 21 = 2. If two dimensions of a 3-dimensional shape are doubled, the volume increases by 22 = 4. If all three dimensions of a 3-D shape are doubled, the volume increases by 23 = 8.
Any closed shape in 2-dimensions can have any area.
Polygons that are rectangular
4
square, rectangle etc. In two dimensions: a quadrilateral. In three dimensions: a tetrahedron.
Area = 2*vertical height
The are no dimensions: the result is a pure number which is 24. "2 by 3 by 4" is a numerical expression: there are no dimensions associated with any of the three numbers and so there are no dimensions in their products.