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A right trapezoid (also called right-angled trapezoid) has two adjacent right angles. [13] Right trapezoids are used in the trapezoidal rule for estimating areas under a curve. An acute trapezoid has two adjacent acute angles on its longer base edge. An obtuse trapezoid on the other hand has one acute and one obtuse angle on each base.
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.
To estimate the area under a curve the trapezoid rule is applied first to one-piece, then two, then four, and so on. One-piece. Note since it starts and ends at zero, this approximation yields zero area. Two-piece Four-piece Eight-piece. After trapezoid rule estimates are obtained, Richardson extrapolation is applied.
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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]
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A trapezoidal decomposition can be constructed by adding the segments from the original subdivision, one by one, in a random order. Initially (before no segments have been added) the trapezoidal decomposition consists of a single trapezoid, the bounding box of the subdivision. Each subsequent step uses a point location query to locate one ...
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.)