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The area of a regular polygon is half its perimeter multiplied by the distance from its center to its sides, and because the sequence tends to a circle, the corresponding formula–that the area is half the circumference times the radius–namely, A = 1 / 2 × 2πr × r, holds for a circle.
where C is the circumference of a circle, d is the diameter, and r is the radius. More generally, = where L and w are, respectively, the perimeter and the width of any curve of constant width. = where A is the area of a circle. More generally, =
Proposition one states: The area of any circle is equal to a right-angled triangle in which one of the sides about the right angle is equal to the radius, and the other to the circumference of the circle. Any circle with a circumference c and a radius r is equal in area with a right triangle with the two legs being c and r.
Area#Area formulas – Size of a two-dimensional surface; Perimeter#Formulas – Path that surrounds an area; List of second moments of area; List of surface-area-to-volume ratios – Surface area per unit volume; List of surface area formulas – Measure of a two-dimensional surface; List of trigonometric identities
The area in circular mils, A, of a circle with a diameter of d mils, is given by the formula: {} = {}. In Canada and the United States, the Canadian Electrical Code (CEC) and the National Electrical Code (NEC), respectively, use the circular mil to define wire sizes larger than 0000 AWG .
The formula for the surface area of a sphere was first obtained by Archimedes in his work On the Sphere and Cylinder. The formula is: [6] A = 4πr 2 (sphere), where r is the radius of the sphere. As with the formula for the area of a circle, any derivation of this formula inherently uses methods similar to calculus.
The ratio of a circle's circumference to its diameter is π (pi), an irrational constant approximately equal to 3.141592654. The ratio of a circle's circumference to its radius is 2 π . [ a ] Thus the circumference C is related to the radius r and diameter d by: C = 2 π r = π d . {\displaystyle C=2\pi r=\pi d.}
The area-equivalent radius of a 2D object is the radius of a circle with the same area as the object Cross sectional area of a trapezoidal open channel, red highlights the wetted perimeter, where water is in contact with the channel. The hydraulic diameter is the equivalent circular configuration with the same circumference as the wetted perimeter.