Divide the below figure into $5$ equal pieces (same shape, same size, possibly reflected).
I believe this is one of Martin Gardner's, but I could not find the source.
The first observation we make is that
the left and right edges are identical
the top and bottom edges are identical
If we then
mark four equidistant points along each horizontal line,
we have constructed the basis for making 5 shapes that are basically
thinner versions of the original shape.
Connecting the dots vertically now subdivides the original shape into 5 equal pieces of the same shape and size.
x-x-x-x-x-x \ \ \ \ \ \ / / / / / / | | | | | | x-x-x-x-x-x
Perhaps the most important observation to make is that
the lattice on which this shape is placed is a visual distraction. Once ignored and only the shape itself is considered, the solution is quite obvious.