Area is a quantity that expresses the extent of a two-dimensional surface or shape, or planar lamina, in the plane. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat. It is the two-dimensional analog of the length of a curve (a one-dimensional concept) or the volume of a solid (a three-dimensional concept).
The area of a shape can be measured by comparing the shape to squares of a fixed size. In the International System of Units (SI), the standard unit of area is the square metre (written as m2), which is the area of a square whose sides are one metre long. A shape with an area of three square metres would have the same area as three such squares. In mathematics, the unit square is defined to have area one, and the area of any other shape or surface is a dimensionless real number.
There are several well-known formulas for the areas of simple shapes such as triangles, rectangles, and circles. Using these formulas, the area of any polygon can be found by dividing the polygon into triangles. For shapes with curved boundary, calculus is usually required to compute the area. Indeed, the problem of determining the area of plane figures was a major motivation for the historical development of calculus.
A checkerboard or chequerboard (see spelling differences) is a board of chequered pattern on which English draughts (checkers) is played. It is an 8×8 board and the 64 squares are of alternating dark and light color, often red and black.
The term checkerboard is also used to denote any rectangular square-tiled board. In this sense it refers not to a physical board as such but to the mathematical abstraction of such a board. The adjective chequered refers to the pattern shown in many locations, such as the checkered flag used to signify the end of a vehicle race or the livery on some emergency service vehicles. However when this pattern is used on such vehicles, in certain countries, it is called a Sillitoe Tartan. The checkerboard is also closely associated with national symbols of the nation of Croatia.
The checkerboard pattern is often associated with the Ska music genre, for breaking the racial barrier between black and whites at the time. A checkerboard marking painted on a hilltop was used as visual guidance on Hong Kong's old Kai Tak Airport. Many taxicabs also use a checkerboard pattern.
A square checkerboard is with an alternating pattern is used for include:
The following games require an 8×8 board and are sometimes played on a chessboard.