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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
Download QR code; Print/export Download as PDF; Printable version; In other projects Wikidata item; ... Lists of shapes cover different types of geometric shape and ...
In geometric measure theory the area formula relates the Hausdorff measure of the image of a Lipschitz map, while accounting for multiplicity, to the integral of the Jacobian of the map. It is one of the fundamental results of the field that has connections, for example, to rectifiability and Sard's theorem .
Euclid proved that the area of a triangle is half that of a parallelogram with the same base and height in his book Elements in 300 BCE. [1] In 499 CE Aryabhata, used this illustrated method in the Aryabhatiya (section 2.6). [2] Although simple, this formula is only useful if the height can be readily found, which is not always the case.
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.
Shoelace scheme for determining the area of a polygon with point coordinates (,),..., (,). The shoelace formula, also known as Gauss's area formula and the surveyor's formula, [1] is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. [2]
For example, if shape has an area of 5 square yards and a perimeter of 5 yards, then it has an area of 45 square feet (4.2 m 2) and a perimeter of 15 feet (since 3 feet = 1 yard and hence 9 square feet = 1 square yard). Moreover, contrary to what the name implies, changing the size while leaving the shape intact changes an "equable shape" into ...
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.
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