# 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) = 10
^{12}square metres (m²)

- US & Imperial Units
- 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

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.