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Area

Related subjects: Mathematics

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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 (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

Area.svg
Common equations for area:
Shape Equation Variables
Square s^2\,\! s is the length of the side of the square.
Regular triangle \frac{\sqrt{3}}{4}s^2\,\! s is the length of one side of the triangle.
Regular hexagon \frac{3\sqrt{3}}{2}s^2\,\! s is the length of one side of the hexagon.
Regular octagon 2(1+\sqrt{2})s^2\,\! s is the length of one side of the octagon.
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 l \cdot w \,\! l and w are the lengths of the rectangle's sides (length and width).
Parallelogram (in general) b \cdot h\,\! b and h are the length of the base and the length of the perpendicular height, respectively.
Rhombus \frac{1}{2}ab a and b are the lengths of the two diagonals of the rhombus.
Triangle \frac{1}{2}b \cdot h \,\! b and h are the base and altitude (measured perpendicular to the base), respectively.
Triangle \frac{1}{2}\cdot a \cdot b \cdot sinC\,\! a and b are any two sides, and C is the angle between them.
Circle \pi r^2 \,\!, or \pi d^2/4 \,\! r is the radius and d the diameter.
Ellipse \pi ab \,\! a and b are the semi-major and semi-minor axes, respectively.
Trapezoid \frac{1}{2}(a+b)h \,\! a and b are the parallel sides and h the distance (height) between the parallels.
Total surface area of a Cylinder 2\pi r^2+2\pi r h \,\! r and h are the radius and height, respectively.
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.
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.
Total surface area of an ellipsoid   See the article.
Circular sector \frac{1}{2} r^2 \theta \,\! r and \theta are the radius and angle (in radians), respectively.
Square to circular area conversion \frac{4}{\pi} A\,\! A is the area of the square in square units.
Circular to square area conversion \frac{1}{4} C\pi\,\! C is the area of the circle in circular units.

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

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