Plano vs. llano
While both plano and llano translate to flat in English, their usage depends on the context of the surface. The word plano is a general term used for physically flat objects, level surfaces, and geometry. On the other hand, the word llano is primarily used to describe geographical terrain, landscapes, and wide open plains without hills or mountains.
Plano
The word plano refers to a surface that is completely level, smooth, and horizontal, without any bumps, curves, or slopes. It is most commonly used to describe objects, architectural elements, geometric planes, and sometimes small areas of land that are perfectly even like a board.
La mesa del comedor tiene una superficie muy plana.
(The dining table has a very flat surface.)
Necesitamos buscar un lugar plano para armar la tienda de campaña.
(We need to find a flat place to set up the tent.)
El techo de ese edificio comercial es completamente plano.
(The roof of that commercial building is completely flat.)
Los televisores modernos tienen pantallas planas que ocupan poco espacio.
(Modern televisions have flat screens that take up little space.)
El doctor le recomendó usar zapatos con suela plana para evitar dolores de espalda.
(The doctor recommended he use shoes with a flat sole to avoid back pain.)
Para que la figura de cristal no se caiga, la base debe ser totalmente plana.
(For the glass figure not to fall, the base must be completely flat.)
Llano
The word llano specifically describes geographical terrain, fields, or landscapes that are flat and even, lacking mountains, hills, or significant elevations. It evokes the image of a wide, open natural plain.
Caminaron durante tres días por el terreno llano bajo el sol brillante.
(They walked for three days across the flat terrain under the bright sun.)
Los caballos corrían libremente por el campo llano sin encontrar obstáculos.
(The horses ran freely across the flat field without encountering obstacles.)
Esta región es conocida por su relieve llano y sus tierras fértiles.
(This region is known for its flat relief and its fertile lands.)
Al salir de la cordillera, llegamos a un territorio llano muy extenso.
(Upon leaving the mountain range, we reached a very extensive flat territory.)
Es bastante difícil esconderse de los depredadores en un paisaje tan llano.
(It is quite hard to hide from predators in such a flat landscape.)
Decidieron construir la nueva granja en el sector más llano del valle.
(They decided to build the new farm in the most flat sector of the valley.)
Summary
In short, use plano when talking about objects, level surfaces, or geometric flatness, such as a table, a roof, or a screen. Choose llano when you are describing wide, flat geographical terrain or natural landscapes that are free from hills and mountains.