“LENGTH”
*in ‘geometric measurements’, length is the ‘most extended dimension’ of an ‘object’*
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in the International System of Quantities, length is any quantity with dimension distance.
in other contexts “length” is the measured dimension of an object.
for example, it is possible to cut a length of a wire which is shorter than wire thickness.
length may be distinguished from height, which is vertical extent, and width or breadth, which are the distance from side to side, measuring across the object at right angles to the length.
length is a measure of one dimension,
whereas area is a measure of two dimensions (length squared)
and volume is a measure of three dimensions (length cubed).
(in most systems of measurement, the unit of length is a base unit, from which other units are defined)
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*AREA*
“ACRE”
the acre is a unit of land area used in the imperial and US customary systems.
It is defined as the area of 1 chain (22 yards) by 1 furlong (220 yards), which is exactly equal to 1⁄640 of a square mile, 43,560 square feet, approximately 4,046.856 m2, or about 40% of a hectare
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 two-dimensional surface of a three-dimensional object. 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.
for a solid shape such as a sphere, cone, or cylinder, the area of its boundary surface is called the surface area. 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.
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, though not every subset is measurable. 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.
(it can be proved that such a function exists)
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*VOLUME*
“QUART”
(a unit of volume)
the quantity of three-dimensional space enclosed by some closed boundary,
for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains.
volume is often quantified numerically using the SI derived unit, the cubic metre.
the volume of a container is generally understood to be the capacity of the container, i. e. the amount of fluid (gas or liquid) that the container could hold, rather than the amount of space the container itself displaces)
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(the ‘boundless 3-dimensional extent’ in which ‘objects’ + ‘events’ have relative ‘position’ + ‘direction’)
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*🌈✨ *TABLE OF CONTENTS* ✨🌷*
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