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This yields as a special case the well-known formula for the area of a triangle, by considering a triangle as a degenerate trapezoid in which one of the parallel sides has shrunk to a point. The 7th-century Indian mathematician Bhāskara I derived the following formula for the area of a trapezoid with consecutive sides a , c , b , d :
In Euclidean geometry, an isosceles trapezoid ... is the semi-perimeter of the trapezoid. This formula is analogous to Heron's formula to compute the area of a ...
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.)
Trapezoid + and are the bases Sources: [1] [2] [3] Three-dimensional shapes. Illustration of the shapes' equation terms ... Perimeter#Formulas – Path that surrounds ...
If the lengths of the three sides are known then Heron's formula can be used: () () where a, b, c are the sides of the triangle, and = (+ +) is half of its perimeter. [2] If an angle and its two included sides are given, the area is 1 2 a b sin ( C ) {\displaystyle {\tfrac {1}{2}}ab\sin(C)} where C is the given angle and a and b are its ...
The formula was described by Albrecht Ludwig Friedrich Meister (1724–1788) in 1769 [4] and is based on the trapezoid formula which was described by Carl Friedrich Gauss and C.G.J. Jacobi. [5] The triangle form of the area formula can be considered to be a special case of Green's theorem.
The area, perimeter, and base can also be related to each other by the equation [24] + = If the base and perimeter are fixed, then this formula determines the area of the resulting isosceles triangle, which is the maximum possible among all triangles with the same base and perimeter. [25]
The wetted perimeter is the perimeter of the cross sectional area that is "wet". [1] The length of line of the intersection of channel wetted surface with a cross sectional plane normal to the flow direction.