Area is a quantity expressing the two-dimensional size of a defined part of a surface, typically a region bounded by a closed curve. Quantity is a kind of property which exists as magnitude or multitude In mathematics the dimension of a Space is roughly defined as the minimum number of Coordinates needed to specify every point within it In Mathematics, specifically in Topology, a surface is a Two-dimensional Manifold. In Mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object The term surface area refers to the total area of the exposed surface of a 3-dimensional solid, such as the sum of the areas of the exposed sides of a polyhedron. What is a polyhedron? We can at least say that a polyhedron is built up from different kinds of element or entity each associated with a different number of dimensions

## Units

Units for measuring surface area include:

Metric
square metre (m²) = SI derived unit
are (a) = 100 square metres (m²)
hectare (ha) = 10,000 square metres (m²)
square kilometre (km²) = 1,000,000 square metres (m²)
square megametre (Mm²) = 1012 square metres
square foot = 144 square inches = 0. M^2 redirects here For other uses see M². CM2 redirects here SI derived units are part of the SI system of measurement units and are derived from the seven SI base units They are derived from SI basic units/defined Conversions One are is equivalent to Metric 00001 km2 (square kilometres 0 Explanation The hectare is commonly used in most countries around the world especially in domains concerned with land planning and management such as Agriculture, Square Kilometre ( US spelling square kilometer) symbol km2, is a decimal multiple of the SI unit of Mega- (symbol M) is an SI prefix in the SI system of units denoting a factor of 106, 1000000 (one Million The square foot is an Imperial unit / US customary unit (non- SI non- metric) of Area, used mainly in the United States 09290304 square metres (m²)
square yard = 9 square feet = 0. The square yard is an imperial / US customary (non- metric) unit of Area, formerly used in most of the English -speaking world but now 83612736 square metres (m²)
square perch = 30. The rod is a unit of Length equal to 55 Yards 11 Cubits 50292 Meters 16 25 square yards = 25. 2928526 square metres (m²)
acre = 160 square perches or 4,840 square yards or 43,560 square feet = 4046. The acre is a unit of Area in a number of different systems including the imperial and U 8564224 square metres (m²)
square mile = 640 acres = 2. The square mile is an imperial and US unit of Area equal the area of a square of one statute mile. 5899881103 square kilometres (km²)

## Useful formulas

Common equations for area:
ShapeEquationVariables
Square$s^2\,\!$s is the length of the side of the square. An equation is a mathematical statement, in symbols, that two things are exactly the same (or equivalent Classification A square (regular Quadrilateral) is a special case of a Rectangle as it has four right angles and equal parallel sides
Regular triangle$\frac{\sqrt{3}}{4}s^2\,\!$s is the length of one side of the triangle. A triangle is one of the basic Shapes of Geometry: a Polygon with three corners or vertices and three sides or edges which are Line
Regular hexagon$\frac{3\sqrt{3}}{2}s^2\,\!$s is the length of one side of the hexagon. Regular hexagon The internal Angles of a regular hexagon (one where all sides and all angles are equal are all 120 ° and the hexagon has 720 degrees
Regular octagon$2(1+\sqrt{2})s^2\,\!$s is the length of one side of the octagon. Regular octagons A regular octagon is an octagon whose sides are all the same length and whose internal angles are all the same size
Any regular polygon$\frac{1}{2}a p \,\!$a is the apothem, or the radius of an inscribed circle in the polygon, and p is the perimeter of the polygon.
Any regular polygon$\frac{P^2/n} {4 \cdot \tan(\pi/n)}\,\!$P is the Perimeter and n is the number of sides.
Any regular polygon (using degree measure)$\frac{P^2/n} {4 \cdot \tan(180^\circ/n)}\,\!$P is the Perimeter and n is the number of sides.
Rectangle$lw \,\!$l and w are the lengths of the rectangle's sides (length and width). In Geometry, a rectangle is defined as a Quadrilateral where all four of its angles are Right angles A rectangle with vertices ABCD would be denoted as
Parallelogram (in general)$bh\,\!$b and h are the length of the base and the length of the perpendicular height, respectively. In Geometry, a parallelogram is a Quadrilateral with two sets of Parallel sides
Rhombus$\frac{1}{2}ab$a and b are the lengths of the two diagonals of the rhombus. In Geometry, a rhombus (from Ancient Greek ῥόμβος - rrhombos “rhombus spinning top” (plural rhombi or rhombuses A diagonal can refer to a line joining two nonconsecutive vertices of a Polygon or Polyhedron, or in contexts any upward or downward sloping line
Triangle$\frac{1}{2}bh \,\!$b and h are the base and altitude (measured perpendicular to the base), respectively. A triangle is one of the basic Shapes of Geometry: a Polygon with three corners or vertices and three sides or edges which are Line The base of any geometric figure is (for Polygons) any side that you wish to measure from or (for Polyhedra) any face that you wish to measure from In Geometry, an altitude of a triangle is a Straight line through a vertex and Perpendicular to (i
Triangle$\frac{1}{2} a b \sin C\,\!$a and b are any two sides, and C is the angle between them. A triangle is one of the basic Shapes of Geometry: a Polygon with three corners or vertices and three sides or edges which are Line
Circle$\pi r^2 ,\,\!$ or $\pi d^2/4 \,\!$r is the radius and d the diameter. Circles are simple Shapes of Euclidean geometry consisting of those points in a plane which are at a constant Distance, called the Geometry, a diameter of a Circle is any straight Line segment that passes through the center of the circle and whose Endpoints are on the
Ellipse$\pi ab \,\!$a and b are the semi-major and semi-minor axes, respectively. In Mathematics, an ellipse (from the Greek ἔλλειψις literally absence) is a Conic section, the locus of points in a In Geometry, the semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae In Geometry, the semi-minor axis (also semiminor axis) is a Line segment associated with most Conic sections (that is with ellipses and
Trapezoid$\frac{1}{2}(a+b)h \,\!$a and b are the parallel sides and h the distance (height) between the parallels. A trapezoid (in North America or a trapezium (in Britain and elsewhere is a Quadrilateral (a closed plane shape with four linear sides that has at least one
Total surface area of a Cylinder$2\pi r^2+2\pi r h \,\!$r and h are the radius and height, respectively. A cylinder is one of the most basic curvilinear geometric shapes the Surface formed by the points at a fixed distance from a given Straight line, the axis
Lateral surface area of a cylinder$2 \pi r h \,\!$r and h are the radius and height, respectively.
Total surface area of a Cone$\pi r (l + r) \,\!$r and l are the radius and slant height, respectively. A cone is a three-dimensional Geometric shape that tapers smoothly from a flat round base to a point called the apex or vertex The slant height of a Right circular cone is the distance from any point on the Circle to the apex of the cone
Lateral surface area of a cone$\pi r l \,\!$r and l are the radius and slant height, respectively.
Total surface area of a Sphere$4\pi r^2\,\!$ or $\pi d^2\,\!$r and d are the radius and diameter, respectively. "Globose" redirects here See also Globose nucleus. A sphere (from Greek σφαίρα - sphaira, "globe
Total surface area of an ellipsoid See the article. An ellipsoid is a type of quadric surface that is a higher dimensional analogue of an Ellipse.
Circular sector$\frac{1}{2} r^2 \theta \,\!$r and θ are the radius and angle (in radians), respectively. A circular sector or circle sector, is the portion of a Circle enclosed by two radii and an arc. The radian is a unit of plane Angle, equal to 180/ π degrees, or about 57
Square to circular area conversion$\frac{4}{\pi} A\,\!$A is the area of the square in square units. Classification A square (regular Quadrilateral) is a special case of a Rectangle as it has four right angles and equal parallel sides Classification A square (regular Quadrilateral) is a special case of a Rectangle as it has four right angles and equal parallel sides
Circular to square area conversion$\frac{1}{4} C\pi\,\!$C is the area of the circle in circular units. Circles are simple Shapes of Euclidean geometry consisting of those points in a plane which are at a constant Distance, called the Circles are simple Shapes of Euclidean geometry consisting of those points in a plane which are at a constant Distance, called the

All of the above calculations show how to find the area of many shapes. The shape ( OE sceap Eng created thing) of an object located in some space refers to the part of space occupied by the object as determined