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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:
The area of an isosceles (or any) trapezoid is equal to the average of the lengths of the base and top ... is the semi-perimeter of the trapezoid.
Similar arguments can be used to find area formulas for the trapezoid [26] as well as more ... The ratio of the area to the square of the perimeter of an ...
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.)
Area Perimeter/Circumference Meanings of symbols ... Trapezoid + and are the bases ... is the base's area and is the prism's height ; Pyramid – , where is ...
The negative trapezoids delete those parts of positive trapezoids, which are outside the polygon. In case of a convex polygon (in the diagram the upper example) this is obvious: The polygon area is the sum of the areas of the positive trapezoids (green edges) minus the areas of the negative trapezoids (red edges). In the non convex case one has ...
Shape Figure ¯ ¯ Area rectangle area: General triangular area + + [1] Isosceles-triangular area: Right-triangular area: Circular area: Quarter-circular area [2]: Semicircular area [3]: Circular sector
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 .