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The midsegment of a trapezoid is one of the two bimedians (the other bimedian divides the trapezoid into equal areas). The height (or altitude) is the perpendicular distance between the bases. In the case that the two bases have different lengths (a ≠ b), the height of a trapezoid h can be determined by the length of its four sides using the ...
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 area of an ellipse is proportional to a rectangle having sides equal to its major and minor axes; The volume of a sphere is 4 times that of a cone having a base of the same radius and height equal to this radius; The volume of a cylinder having a height equal to its diameter is 3/2 that of a sphere having the same diameter;
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.)
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
If is the radius of the incircle of the triangle, then the triangle can be broken into three triangles of equal altitude and bases , , and . Their combined area is A = 1 2 a r + 1 2 b r + 1 2 c r = r s , {\displaystyle A={\tfrac {1}{2}}ar+{\tfrac {1}{2}}br+{\tfrac {1}{2}}cr=rs,} where s = 1 2 ( a + b + c ...
Cross sectional area of a trapezoidal open channel, red highlights wetted perimeter Change of wetted perimeter (blue) of trapezoidal canal as a function of angle ψ.. The wetted perimeter is the perimeter of the cross sectional area that is "wet". [1]