Area
2008/9 Schools Wikipedia Selection. Related subjects: Mathematics
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 | s is the length of the side of the square. | |
Regular triangle | s is the length of one side of the triangle. | |
Regular hexagon | s is the length of one side of the hexagon. | |
Regular octagon | s is the length of one side of the octagon. | |
Any regular polygon | 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 | P is the Perimeter and n is the number of sides. | |
Any regular polygon (using degree measure) | P is the Perimeter and n is the number of sides. | |
Rectangle | l and w are the lengths of the rectangle's sides (length and width). | |
Parallelogram (in general) | b and h are the length of the base and the length of the perpendicular height, respectively. | |
Rhombus | a and b are the lengths of the two diagonals of the rhombus. | |
Triangle | b and h are the base and altitude (measured perpendicular to the base), respectively. | |
Triangle | a and b are any two sides, and C is the angle between them. | |
Circle | , or | r is the radius and d the diameter. |
Ellipse | a and b are the semi-major and semi-minor axes, respectively. | |
Trapezoid | a and b are the parallel sides and h the distance (height) between the parallels. | |
Total surface area of a Cylinder | r and h are the radius and height, respectively. | |
Lateral surface area of a cylinder | r and h are the radius and height, respectively. | |
Total surface area of a Cone | r and l are the radius and slant height, respectively. | |
Lateral surface area of a cone | r and l are the radius and slant height, respectively. | |
Total surface area of a Sphere | or | r and d are the radius and diameter, respectively. |
Total surface area of an ellipsoid | See the article. | |
Circular sector | r and θ are the radius and angle (in radians), respectively. | |
Square to circular area conversion | A is the area of the square in square units. | |
Circular to square area conversion | C is the area of the circle in circular units. |
All of the above calculations show how to find the area of many shapes.