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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.
and the formula for the area A of a circular sector of radius r and with central angle of measure 𝜃 is =. In the special case 𝜃 = 2 π, these formulae yield the circumference of a complete circle and area of a complete disc, respectively.
Area of a circle; Circumference; Use in other formulae; ... where SV is the surface volume of a 3-sphere and r is the ... More formulas of this nature can be given, ...
The arc length, from the familiar geometry of a circle, is = The area a of the circular segment is equal to the area of the circular sector minus the area of the triangular portion (using the double angle formula to get an equation in terms of ):
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; List of volume formulas – Quantity of three-dimensional space
The formula for the area of a circle (more properly called the area enclosed by a circle or the area of a disk) is based on a similar method. Given a circle of radius r , it is possible to partition the circle into sectors , as shown in the figure to the right.
The circumference of a circle with radius r is 2πr. [155] The area of a circle with radius r is πr 2. The area of an ellipse with semi-major axis a and semi-minor axis b is πab. [156] The volume of a sphere with radius r is 4 / 3 πr 3. The surface area of a sphere with radius r is 4πr 2.
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.