The Mexican Cession or the Mexican States of Alta California and Nuevo Mexico.
Central Mexican Plateau or Mexican Altiplano.
Before the Mexican Revolution that gained independence of Mexico from Spain, Spain laid claim to the area along the North American Pacific coast that includes what is now the state of California.
The Peninsula Of Yucatan
it is from the more southern area of mexico
The Texcoco valley, in the Mexican Central Plateau.
It is the Central Mexican Plateau or Mexican Altiplano.
The Mexican Altiplano.
It lost about half of its land area.
Mexican foods and celebrations are popular throughout the area
Yes, but only a fraction of it. The whole county of Uinta and almost half of Lincoln and Sweetwater counties were part of Mexico. The Utah border would give you an indication of the limits of former Mexican territory, as such area is "overlapped" between both states.
The large, flat center of Mexico is called a plateau. This area is also called the land of many climates because of the constantly changing weather pattern in the area.