If you draw the diagonal of a trapezoid the polygon is split into two smaller poligons

no, you get two triangles, since no piece of both bases appears in either polygon.

. The resulting smaller polygons are a triangle and a smaller trapezoid. The diagonal connects two non-parallel sides of the trapezoid and divides it into two parts. The triangle and trapezoid that are created will have different shapes and sizes, depending on the specific dimensions of the original trapezoid.

Apologies for the mistake. You are correct. When drawing the diagonal of a trapezoid, the resulting smaller polygons are two triangles. No piece of either base of the trapezoid appears in either of the triangles formed by the diagonal. Thank you for pointing out the error.