
In general, area in higher mathematics is seen as a special case of volume for two-dimensional regions. In analysis, the area of a subset of the plane is defined using Lebesgue measure, though not every subset is measurable. In addition to its obvious importance in geometry and calculus, area is related to the definition of determinants in linear algebra, and is a basic property of surfaces in differential geometry. Formulas for the surface areas of simple shapes were computed by the ancient Greeks, but computing the surface area of a more complicated shape usually requires multivariable calculus.Īrea plays an important role in modern mathematics. įor a solid shape such as a sphere, cone, or cylinder, the area of its boundary surface is called the surface area.

Indeed, the problem of determining the area of plane figures was a major motivation for the historical development of calculus. For shapes with curved boundary, calculus is usually required to compute the area.

Using these formulas, the area of any polygon can be found by dividing the polygon into triangles. There are several well-known formulas for the areas of simple shapes such as triangles, rectangles, and circles. 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. A shape with an area of three square metres would have the same area as three such squares. In the International System of Units (SI), the standard unit of area is the square metre (written as m 2), which is the area of a square whose sides are one metre long. The area of a shape can be measured by comparing the shape to squares of a fixed size. Two different regions may have the same area (as in squaring the circle) by synecdoche, "area" sometimes is used to refer to the region, as in a " polygonal area". It is the two-dimensional analogue of the length of a curve (a one-dimensional concept) or the volume of a solid (a three-dimensional concept). 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. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object. Please enable Javascript in your browser to use this River Cross Section calculator.Area is the measure of a region's size on a surface. Hover over the image to display the data. A menu appears above the cross section offering several options, including downloading an image. The 'Open Cross Section' button will open your river cross section in a new window. Select the type of cross section required (drawn with rounded or straight lines) and click the 'Calculate' button to calculate your data. The 'Customise' button opens options to change the cross section title and set the X axis range.Įnter your fieldwork results in the calculator below. Manning's n can be used to calculate river velocity. The 'More' button opens more calculation options, including river discharge.
#CROSS SECTIONAL AREA OF RECTANGLE FORMULA DOWNLOAD#
Download an image of your cross section and print the data calculations used to construct and analyse it.

Braided channel cross sections can be created by entering land as negative data.

River Cross Section Creator and CalculatorĮnter your river data to quickly make a river cross section and calculate the cross sectional area, wetted perimeter and hydraulic radius.
