Area in the context of Volume

In photography, exposure is the amount of light per unit area reaching a frame of photographic film or the surface of an electronic image sensor. It is determined by exposure time, lens f-number, and scene luminance. Exposure is measured in units of lux-seconds (symbol lx⋅s), and can be computed from exposure value (EV) and scene luminance in a specified region.

An "exposure" is a single shutter cycle. For example, a long exposure refers to a single, long shutter cycle to gather enough dim light, whereas a multiple exposure involves a series of shutter cycles, effectively layering a series of photographs in one image. The accumulated photometric exposure (H_v) is the same so long as the total exposure time is the same.

The square kilometre (square kilometer in American spelling; symbol: km) is a multiple of the square metre, the SI unit of area or surface area. In the SI unit of area (m), 1 km is equal to 1M(m).

The hectare (/ˈhɛktɛər, -tɑːr/; SI symbol: ha) is a non-SI metric unit of area equal to a square with 100-metre sides (1 hm), that is, 10,000 square metres (10,000 m), and is primarily used in the measurement of land. There are 100 hectares in one square kilometre. An acre is about 0.405 hectares and thus one hectare is about 2.47 acres.

In 1795, when the metric system was introduced, the are was defined as 100 square metres, or one square decametre, and the hectare ("hecto-" + "are") was thus 100 ares or ⁠1/100⁠ km (10000 square metres). When the metric system was further rationalised in 1960, resulting in the International System of Units (SI), the are was not included as a recognised unit. The hectare, however, remains as a non-SI unit accepted for use with the SI and whose use is "expected to continue indefinitely". Though the dekare/decare daa (1000 m) and are (100 m) are not officially "accepted for use", they are still used in some contexts.

Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations.

Originally called infinitesimal calculus or "the calculus of infinitesimals", it has two major branches, differential calculus and integral calculus. The former concerns instantaneous rates of change, and the slopes of curves, while the latter concerns accumulation of quantities, and areas under or between curves. These two branches are related to each other by the fundamental theorem of calculus. They make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit. It is the "mathematical backbone" for dealing with problems where variables change with time or another reference variable. It has also been called "the basic instrument of physical science".

The method of exhaustion (Latin: methodus exhaustionis) is a method of finding the area of a shape by inscribing inside it a sequence of polygons (one at a time) whose areas converge to the area of the containing shape. If the sequence is correctly constructed, the difference in area between the nth polygon and the containing shape will become arbitrarily small as n becomes large. As this difference becomes arbitrarily small, the possible values for the area of the shape are systematically "exhausted" by the lower bound areas successively established by the sequence members.

The method of exhaustion typically required a form of proof by contradiction, known as reductio ad absurdum. This amounts to finding an area of a region by first comparing it to the area of a second region, which can be "exhausted" so that its area becomes arbitrarily close to the true area. The proof involves assuming that the true area is greater than the second area, proving that assertion false, assuming it is less than the second area, then proving that assertion false, too.

In geometry, the area enclosed by a circle of radius r is πr. Here, the Greek letter π represents the constant ratio of the circumference of any circle to its diameter, approximately equal to 3.14159.

One method of deriving this formula, which originated with Archimedes, involves viewing the circle as the limit of a sequence of regular polygons with an increasing number of sides. The area of a regular polygon is half its perimeter multiplied by the distance from its center to its sides, and because the sequence tends to a circle, the corresponding formula–that the area is half the circumference times the radius–namely, A = ⁠1/2⁠ × 2πr × r, holds for a circle.

The surface area (symbol A) of a solid object is a measure of the total area that the surface of the object occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of arc length of one-dimensional curves, or of the surface area for polyhedra (i.e., objects with flat polygonal faces), for which the surface area is the sum of the areas of its faces. Smooth surfaces, such as a sphere, are assigned surface area using their representation as parametric surfaces. This definition of surface area is based on methods of infinitesimal calculus and involves partial derivatives and double integration.

A general definition of surface area was sought by Henri Lebesgue and Hermann Minkowski at the turn of the twentieth century. Their work led to the development of geometric measure theory, which studies various notions of surface area for irregular objects of any dimension. An important example is the Minkowski content of a surface.

In geometry, a square is a regular quadrilateral. It has four straight sides of equal length and four equal angles. Squares are special cases of rectangles, which have four equal angles, and of rhombuses, which have four equal sides. As with all rectangles, a square's angles are right angles (90 degrees, or π/2 radians), making adjacent sides perpendicular. The area of a square is the side length multiplied by itself, and so in algebra, multiplying a number by itself is called squaring.

Equal squares can tile the plane edge-to-edge in the square tiling. Square tilings are ubiquitous in tiled floors and walls, graph paper, image pixels, and game boards. Square shapes are also often seen in building floor plans, origami paper, food servings, in graphic design and heraldry, and in instant photos and fine art.

In Euclidean geometry, a regular polygon is a polygon that is direct equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Regular polygons may be either convex or star. In the limit, a sequence of regular polygons with an increasing number of sides approximates a circle, if the perimeter or area is fixed, or a regular apeirogon (effectively a straight line), if the edge length is fixed.

Following are two lists of terrestrial lakes that have surface areas of more than approximately 3,000 square kilometres (1,200 sq mi), ranked by area, excluding reservoirs and lagoons.

The area of some lakes can vary over time, either seasonally or from year to year. This is especially true of salt lakes in arid climates.This list therefore excludes seasonal lakes such as Kati Thanda–Lake Eyre (maximum area 9,500 km, 3,700 sq mi), Mar Chiquita Lake (Córdoba) (maximum area 6,000 km, 2,300 sq mi), Chott el Djerid (up to 7,000 km, 2,700 sq mi, Lake Torrens (maximum area 5,745 km, 2,218 sq mi) and Great Salt Lake (maximum area, 1988, 8,500 km, 3,300 sq mi).

Size in general is the magnitude or dimensions of a thing. More specifically, geometrical size (or spatial size) can refer to three geometrical measures: length, area, or volume. Length can be generalized to other linear dimensions (width, height, diameter, perimeter). Size can also be measured in terms of mass, especially when assuming a density range.

In mathematical terms, "size is a concept abstracted from the process of measuring by comparing a longer to a shorter". Size is determined by the process of comparing or measuring objects, which results in the determination of the magnitude of a quantity, such as length or mass, relative to a unit of measurement. Such a magnitude is usually expressed as a numerical value of units on a previously established spatial scale, such as meters or inches.

Grammage and basis weight, in the pulp and paper industry, are the area density of a paper product, that is, its mass per unit of area. Two ways of expressing the area density of a paper product are commonly used:

• Expressed in grams (g) per square metre (g/m), regardless of its thickness (caliper) (known as grammage). This is the measure used in most parts of the world. It is often notated as gsm on paper product labels and spec sheets.
• Expressed in terms of the mass per number of sheets of a specific paper size (known as basis weight). The convention used in the United States and a few other countries using US-standard paper sizes is pounds (lb) per ream of 500 (or in some cases 1000) sheets of a given (raw, still uncut) basis size. The traditional British practice is pounds per ream of 480, 500, 504, or 516 sheets of a given basis size. Japanese paper is expressed as the weight in kilograms (kg) per 1,000 sheets.

In radiometry, photometry, and color science, a spectral power distribution (SPD) measurement describes the power per unit area per unit wavelength of an illumination (radiant exitance). More generally, the term spectral power distribution can refer to the concentration, as a function of wavelength, of any radiometric or photometric quantity (e.g. radiant energy, radiant flux, radiant intensity, radiance, irradiance, radiant exitance, radiosity, luminance, luminous flux, luminous intensity, illuminance, luminous emittance).

Knowledge of the SPD is crucial for optical-sensor system applications. Optical properties such as transmittance, reflectivity, and absorbance as well as the sensor response are typically dependent on the incident wavelength.

In physics and many other areas of science and engineering the intensity or flux of radiant energy is the power transferred per unit area, where the area is measured on the plane perpendicular to the direction of propagation of the energy. In the SI system, it has units watts per square metre (W/m), or kg⋅s in base units. Intensity is used most frequently with waves such as acoustic waves (sound), matter waves such as electrons in electron microscopes, and electromagnetic waves such as light or radio waves, in which case the average power transfer over one period of the wave is used. Intensity can be applied to other circumstances where energy is transferred. For example, one could calculate the intensity of the kinetic energy carried by drops of water from a garden sprinkler.

The word "intensity" as used here is not synonymous with "strength", "amplitude", "magnitude", or "level", as it sometimes is in colloquial speech.

In mathematics, an integral is the continuous analog of a sum, and is used to calculate areas, volumes, and their generalizations. Integration, the process of computing an integral, is one of the two fundamental operations of calculus, the other being differentiation. Integration was initially used to solve problems in mathematics and physics, such as finding the area under a curve, or determining displacement from velocity. Usage of integration expanded to a wide variety of scientific fields thereafter.

A definite integral computes the signed area of the region in the plane that is bounded by the graph of a given function between two points in the real line. Conventionally, areas above the horizontal axis of the plane are positive while areas below are negative. Integrals also refer to the concept of an antiderivative, a function whose derivative is the given function; in this case, they are also called indefinite integrals. The fundamental theorem of calculus relates definite integration to differentiation and provides a method to compute the definite integral of a function when its antiderivative is known; differentiation and integration are inverse operations.

In mathematics, the concept of a measure is a generalization and formalization of geometrical measures (length, area, volume) and other common notions, such as magnitude, mass, and probability of events. These seemingly distinct concepts have many similarities and can often be treated together in a single mathematical context. Measures are foundational in probability theory, integration theory, and can be generalized to assume negative values, as with electrical charge. Far-reaching generalizations (such as spectral measures and projection-valued measures) of measure are widely used in quantum physics and physics in general.

The intuition behind this concept dates back to Ancient Greece, when Archimedes tried to calculate the area of a circle. But it was not until the late 19th and early 20th centuries that measure theory became a branch of mathematics. The foundations of modern measure theory were laid in the works of Émile Borel, Henri Lebesgue, Nikolai Luzin, Johann Radon, Constantin Carathéodory, and Maurice Fréchet, among others. According to Thomas W. Hawkins Jr., "It was primarily through the theory of multiple integrals and, in particular the work of Camille Jordan that the importance of the notion of measurability was first recognized."

Churches can be measured and compared in several ways. These include area, volume, length, width, height, or capacity. Several churches individually claim to be "the largest church", which may be due to any one of these criteria.