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For example, the perimeter of a rectangle of width 0.001 and length 1000 is slightly above 2000, while the perimeter of a rectangle of width 0.5 and length 2 is 5. Both areas are equal to 1. Proclus (5th century) reported that Greek peasants "fairly" parted fields relying on their perimeters. [ 2 ]
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
In Euclidean plane geometry, a rectangle is a rectilinear convex polygon or a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a parallelogram containing a right angle. A rectangle with four sides of equal length is a square.
The only equable rectangles with integer sides are the 4 × 4 square and the 3 × 6 rectangle. [4] An integer rectangle is a special type of polyomino, and more generally there exist polyominoes with equal area and perimeter for any even integer area greater than or equal to 16. For smaller areas, the perimeter of a polyomino must exceed its area.
The apothem a can be used to find the area of any regular n-sided polygon of side length s according to the following formula, which also states that the area is equal to the apothem multiplied by half the perimeter since ns = p.
If a figure is both a rectangle (right angles) and a rhombus (equal edge lengths), then it is a square. A square has a larger area than any other quadrilateral with the same perimeter. [7] A square tiling is one of three regular tilings of the plane (the others are the equilateral triangle and the regular hexagon).
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