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In geometry, a trapezoid (/ ˈ t r æ p ə z ɔɪ d /) in North American English, or trapezium ... where K is the area of the quadrilateral. [16]: Thm.8 ...
The area of an isosceles (or any) trapezoid is equal to the average of the lengths of the base and top (the parallel sides) times the height. In the adjacent diagram, if we write AD = a , and BC = b , and the height h is the length of a line segment between AD and BC that is perpendicular to them, then the area K is
The formula for the area of a trapezoid can be simplified using Pitot's theorem to get a formula for the area of a tangential trapezoid. If the bases have lengths a, b, and any one of the other two sides has length c, then the area K is given by the formula [2] (This formula can be used only in cases where the bases are parallel.)
Trapezium, plural trapezia, may refer to: Trapezium, in British and other forms of English, a trapezoid , a quadrilateral that has exactly one pair of parallel sides Trapezium, in North American English, an irregular quadrilateral with no sides parallel
The area K of a tangential quadrilateral is given by K = r ⋅ s , {\displaystyle \displaystyle K=r\cdot s,} where s is the semiperimeter and r is the inradius .
In calculus, the trapezoidal rule (also known as the trapezoid rule or trapezium rule) [a] is a technique for numerical integration, i.e., approximating the definite integral: (). The trapezoidal rule works by approximating the region under the graph of the function f ( x ) {\displaystyle f(x)} as a trapezoid and calculating its area.
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]
giving the basic form of Brahmagupta's formula. It follows from the latter equation that the area of a cyclic quadrilateral is the maximum possible area for any quadrilateral with the given side lengths. A related formula, which was proved by Coolidge, also gives the area of a general convex