Area is a quantity expressing the twodimensional 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 3dimensional solid, such as the sum of the areas of the exposed sides of a polyhedron. Area is an important invariant in the differential geometry of surfaces.^{[1]}
Contents 
Units for measuring area, with exact conversions, include:
Shape  Formula  Variables 

Regular triangle (equilateral triangle)  s is the length of one side of the triangle.  
Triangle  s is half the perimeter, a, b and c are the length of each side.  
Triangle  a and b are any two sides, and C is the angle between them.  
Triangle  b and h are the base and altitude (measured perpendicular to the base), respectively.  
Square  s is the length of one side of the square.  
Rectangle  l and w are the lengths of the rectangle's sides (length and width).  
Rhombus  a and b are the lengths of the two diagonals of the rhombus.  
Parallelogram  b is the length of the base and h is the perpendicular height.  
Trapezoid  a and b are the parallel sides and h the distance (height) between the parallels.  
Regular hexagon  s is the length of one side of the hexagon.  
Regular octagon  s is the length of one side of the octagon.  
Regular polygon  s is the sidelength and n is the number of sides.  
a is the apothem, or the radius of an inscribed circle in the polygon, and p is the perimeter of the polygon.  
Circle  r is the radius and d the diameter.  
Circular sector  r and θ are the radius and angle (in radians), respectively.  
Ellipse  a and b are the semimajor and semiminor axes, respectively.  
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  r and d are the radius and diameter, respectively.  
Total surface area of an ellipsoid  See the article.  
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. 
The above calculations show how to find the area of many common shapes.
The area of irregular polygons can be calculated using the "Surveyor's formula".^{[2]}
(see Green's theorem)
The general formula for the surface area of the graph of a continuously differentiable function z = f(x,y), where and D is a region in the xyplane with the smooth boundary:
Even more general formula for the area of the graph of a parametric surface in the vector form where is a continuously differentiable vector function of :
Given a wire contour, the surface of least area spanning ("filling") it is a minimal surface. Familiar examples include soap bubbles.
The question of the filling area of the Riemannian circle remains open.
