(1) A numerical measure of the amount of surface contained within a closed curve on a surface. It is usually referred to as the area of the figure if the surface is flat. Area is a function of the shape of the surface, the shape of the curve, and the location of the curve on the surface. On a plane, the area within a rectangle is defined as the product of the lengths of two adjacent sides of the rect-angle. The area within a triangle can be shown to be equivalent to the area within a rectangle having the base of the triangle as one side and a line half as long as the height of the triangle as the other side. The area within a more complex, straight sided figure can be found by dividing the figure into rectangles and triangles and taking the sum of the areas of these smaller figures. The planar areas within some simple closed curves such as the circle and ellipse can be found by direct integration (quadrature), but areas of planar surfaces within more complex curves must usually be found by numerical integration. Numerical integration consists basically of dividing a figure geometrically into rectangles and triangles whose sides are nearly straight, summing the areas, and finding the limiting value of the sum as the subdivision becomes finer and finer. The area of a curved surface is similarly found, by direct integration if the surface is a simple one, or by numerical integration if the surface is complex. Again, this is equivalent to subdividing the surface into small three sided and four sided figures bounded by curves, estimating the areas of these curved figures, summing the areas, and finding the limit as the subdivision becomes finer and finer and the small figures come closer and closer to becoming (planar) rectangles and triangles. This mathematical process has been mechanized, and instruments such as the planimeter allow one to find the area contained by a closed curve by tracing the perimeter of that curve. For many purposes, however, the area of a small region can be found well enough by covering a map of the region by a rectangular grid and summing over the areas of the squares and triangles formed by the grid and the boundary of the region. Area is almost always given as the area of a planar rectangle having the same area as the surface in question, and the area of a planar rectangle is given as the number of squares of unit length on a side that it can contain. The area of any surface is therefore given in terms of the areas of unit squares. The two units of area in almost universal use today are the square meter (the planar area contained within a square 1 meter on a side) and the hectare (the planar area contained within a square 100 meters on a side). In the United States of America, the square foot and the square inch are used for the measures of small regions. For large regions, the acre or square mile is used. For areas of small, circular figures, the circular inch (the area of a circle 1 inch in diameter) and the circular mil (the area within a circle 0. 001 inch in diameter) are sometimes used. (2) That portion of a surface bounded by a closed curve. It differs from region in that the latter does not have the connotation of numerical value. (3) Some clearly defined space. Approximately equivalent to region. (real estate) - A parcel assumed to be level and at mean sea level. These assumptions are used to get consistent descriptions of land.