Area

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Area is a quantity expressing the two-dimensional size of a defined part of a surface, typically a region bounded by a closed curve. 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.

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 = 0.09290304 square metres (m²)
square yard = 9 square feet = 0.83612736 square metres (m²)
square perch = 30.25 square yards = 25.2928526 square metres (m²)
acre = 160 square perches or 4,840 square yards or 43,560 square feet = 4046.8564224 square metres (m²)
square mile = 640 acres = 2.5899881103 square kilometres (km²)

Useful formulas

Common equations for area:
Shape Equation Variables
Square is the length of the side of the square.
Regular triangle is the length of one side of the triangle.
Regular hexagon is the length of one side of the hexagon.
Regular octagon is the length of one side of the octagon.
Any regular polygon is the apothem, or the radius of an inscribed circle in the polygon, and is the perimeter of the polygon.
Any regular polygon is the Perimeter and is the number of sides.
Any regular polygon (using degree measure) is the Perimeter and is the number of sides.
Rectangle and are the lengths of the rectangle's sides (length and width).
Parallelogram (in general) and are the length of the base and the length of the perpendicular height, respectively.
Rhombus and are the lengths of the two diagonals of the rhombus.
Triangle and are the base and altitude (measured perpendicular to the base), respectively.
Triangle and are any two sides, and is the angle between them.
Circle or is the radius and the diameter.
Ellipse and are the semi-major and semi-minor axes, respectively.
Trapezoid and are the parallel sides and the distance (height) between the parallels.
Total surface area of a Cylinder and are the radius and height, respectively.
Lateral surface area of a cylinder and are the radius and height, respectively.
Total surface area of a Cone and are the radius and slant height, respectively.
Lateral surface area of a cone and are the radius and slant height, respectively.
Total surface area of a Sphere or and are the radius and diameter, respectively.
Total surface area of an ellipsoid   See the article.
Circular sector and are the radius and angle (in radians), respectively.
Square to circular area conversion is the area of the square in square units.
Circular to square area conversion is the area of the circle in circular units.

All of the above calculations show how to find the area of many shapes.

See also

External links

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