1.
Centare
–
The hectare is an SI accepted metric system unit of area equal to 100 ares and primarily used in the measurement of land as a metric replacement for the imperial acre. An acre is about 0.405 hectare and one hectare contains about 2.47 acres, in 1795, when the metric system was introduced, the are was defined as 100 square metres and the hectare was thus 100 ares or 1⁄100 km2. When the metric system was further rationalised in 1960, resulting in the International System of Units, the are was not included as a recognised unit. The hectare, however, remains as a non-SI unit accepted for use with the SI units, the metric system of measurement was first given a legal basis in 1795 by the French Revolutionary government. At the first meeting of the CGPM in 1889 when a new standard metre, manufactured by Johnson Matthey & Co of London was adopted, in 1960, when the metric system was updated as the International System of Units, the are did not receive international recognition. The units that were catalogued replicated the recommendations of the CGPM, many farmers, especially older ones, still use the acre for everyday calculations, and convert to hectares only for official paperwork. Farm fields can have long histories which are resistant to change, with names such as the six acre field stretching back hundreds of years. The names centiare, deciare, decare and hectare are derived by adding the standard metric prefixes to the base unit of area. The centiare is a synonym for one square metre, the deciare is ten square metres. The are is a unit of area, equal to 100 square metres and it was defined by older forms of the metric system, but is now outside of the modern International System of Units. It is commonly used to measure real estate, in particular in Indonesia, India, and in French-, Portuguese-, Slovakian-, Serbian-, Czech-, Polish-, Dutch-, in Russia and other former Soviet Union states, the are is called sotka. It is used to describe the size of suburban dacha or allotment garden plots or small city parks where the hectare would be too large, the decare is derived from deka, the prefix for 10 and are, and is equal to 10 ares or 1000 square metres. It is used in Norway and in the former Ottoman areas of the Middle East, the hectare, although not strictly a unit of SI, is the only named unit of area that is accepted for use within the SI. The United Kingdom, United States, Burma, and to some extent Canada instead use the acre, others, such as South Africa, published conversion factors which were to be used particularly when preparing consolidation diagrams by compilation. In many countries, metrication redefined or clarified existing measures in terms of metric units, non-SI units accepted for use with the International System of Units

Centare
–

Trafalgar Square has an area of about one hectare.

Centare
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Definition of a hectare and of an are.

Centare
–

Waikato Stadium – Hamilton, New Zealand

Centare
–

The Statue of Liberty –

New York Harbor
2.
Standard metre
–
The metre or meter, is the base unit of length in the International System of Units. The metre is defined as the length of the path travelled by light in a vacuum in 1/299792458 seconds, the metre was originally defined in 1793 as one ten-millionth of the distance from the equator to the North Pole. In 1799, it was redefined in terms of a metre bar. In 1960, the metre was redefined in terms of a number of wavelengths of a certain emission line of krypton-86. In 1983, the current definition was adopted, the imperial inch is defined as 0.0254 metres. One metre is about 3 3⁄8 inches longer than a yard, Metre is the standard spelling of the metric unit for length in nearly all English-speaking nations except the United States and the Philippines, which use meter. Measuring devices are spelled -meter in all variants of English, the suffix -meter has the same Greek origin as the unit of length. This range of uses is found in Latin, French, English. Thus calls for measurement and moderation. In 1668 the English cleric and philosopher John Wilkins proposed in an essay a decimal-based unit of length, as a result of the French Revolution, the French Academy of Sciences charged a commission with determining a single scale for all measures. In 1668, Wilkins proposed using Christopher Wrens suggestion of defining the metre using a pendulum with a length which produced a half-period of one second, christiaan Huygens had observed that length to be 38 Rijnland inches or 39.26 English inches. This is the equivalent of what is now known to be 997 mm, no official action was taken regarding this suggestion. In the 18th century, there were two approaches to the definition of the unit of length. One favoured Wilkins approach, to define the metre in terms of the length of a pendulum which produced a half-period of one second. The other approach was to define the metre as one ten-millionth of the length of a quadrant along the Earths meridian, that is, the distance from the Equator to the North Pole. This means that the quadrant would have defined as exactly 10000000 metres at that time. To establish a universally accepted foundation for the definition of the metre, more measurements of this meridian were needed. This portion of the meridian, assumed to be the length as the Paris meridian, was to serve as the basis for the length of the half meridian connecting the North Pole with the Equator

Standard metre
–

Belfry, Dunkirk —the northern end of the meridian arc

Standard metre
–

Fortress of Montjuïc —the southerly end of the meridian arc

Standard metre
–
Creating the metre-alloy in 1874 at the Conservatoire des Arts et Métiers. Present Henri Tresca, George Matthey, Saint-Claire Deville and Debray

Standard metre
–
Closeup of National Prototype Metre Bar No. 27, made in 1889 by the

International Bureau of Weights and Measures (BIPM) and given to the United States, which served as the standard for defining all units of length in the US from 1893 to 1960

3.
Area
–
Area is the quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane. Surface area is its analog on the surface of a three-dimensional object. It is the analog of the length of a curve or the volume of a solid. The area of a shape can be measured by comparing the shape to squares of a fixed size, in the International System of Units, the standard unit of area is the square metre, 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 area as three such squares. In mathematics, the square is defined to have area one. There are several formulas for the areas of simple shapes such as triangles, rectangles. 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 motivation for the historical development of calculus. For a solid such as a sphere, cone, or cylinder. Formulas for the areas of simple shapes were computed by the ancient Greeks. Area plays an important role in modern mathematics, 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. In analysis, the area of a subset of the plane is defined using Lebesgue measure, in general, area in higher mathematics is seen as a special case of volume for two-dimensional regions. Area can be defined through the use of axioms, defining it as a function of a collection of certain plane figures to the set of real numbers and it can be proved that such a function exists. An approach to defining what is meant by area is through axioms, area can be defined as a function from a collection M of special kind of plane figures to the set of real numbers which satisfies the following properties, For all S in M, a ≥0. If S and T are in M then so are S ∪ T and S ∩ T, if S and T are in M with S ⊆ T then T − S is in M and a = a − a. If a set S is in M and S is congruent to T then T is also in M, every rectangle R is in M. If the rectangle has length h and breadth k then a = hk, let Q be a set enclosed between two step regions S and T

Area
–
A square metre

quadrat made of PVC pipe.

Area
–
The combined area of these three

shapes is

approximately 15.57

squares.

4.
Km^2
–
Square kilometre or square kilometer, symbol km2, is a multiple of the square metre, the SI unit of area or surface area. For example,3 km2 is equal to 3×2 =3,000,000 m2, topographical map grids are worked out in metres, with the grid lines being 1,000 metres apart. 1,100,000 maps are divided into squares representing 1 km2, each square on the map being one square centimetre in area, for 1,50,000 maps, the grid lines are 2 cm apart. Each square on the map is 2 cm by 2 cm, for 1,25,000 maps, the grid lines are 4 cm apart. Each square on the map is 4 cm by 4 cm, in each case, the grid lines enclose one square kilometre. The area enclosed by the walls of many European medieval cities were about one square kilometre, the approximate area of the old walled cities can often be worked out by fitting the course of the wall to a rectangle or an oval. Examples include Delft, Netherlands 52°0′54″N 4°21′34″E The walled city of Delft was approximately rectangular, the approximate length of rectangle was about 1.30 kilometres. The approximate width of the rectangle was about 0.75 kilometres, a perfect rectangle with these measurements has an area of 1. 30×0.75 =0.9 km2 Lucca 43°50′38″N 10°30′2″E The medieval city is roughly rectangular with rounded north-east and north-west corners. The maximum distance from east to west is 1.36 kilometres, the maximum distance from north to south is 0.80 kilometres. A perfect rectangle of these dimensions would be 1. 36×0.80 =1.088 km2, Brugge 51°12′39″N 3°13′28″E The medieval city of Brugge, a major centre in Flanders, was roughly oval or elliptical in shape with the longer or semi-major axis running north and south. The maximum distance from north to south is 2.53 kilometres, the maximum distance from east to west is 1.81 kilometres. A perfect ellipse of these dimensions would be 2.53 ×1.81 × =3.597 km2. Chester United Kingdom 53°12′1″N 2°52′45″W Chester is one of the smaller English cities that has a city wall. The distance from Northgate to Watergate is about 855 metres. The distance from Eastgate to Westgate is about 589 metres, a perfect rectangle of these dimensions would be × =0.504 km2. Parks come in all sizes, a few are almost exactly one kilometre in area. Here are some examples, Riverside Country Park, UK. Brierley Forest Park, rio de Los Angeles State Park, California, USA Jones County Central Park, Iowa, USA. Using the figures published by golf course architects Crafter and Mogford, assuming a 6,000 metres 18-hole course, an area of 80 hectares needs to be allocated for the course itself

Km^2
–
Part of an Ordnance Survey map, published 1952. The grid lines are at one kilometre intervals giving each square an area of one square kilometre. The map shows that the area of the island is about two square kilometres.