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2. Brahmagupta's formula - Wikipedia

   en.wikipedia.org/wiki/Brahmagupta's_formula

   This formula generalizes Heron's formula for the area of a triangle. A triangle may be regarded as a quadrilateral with one side of length zero. From this perspective, as d approaches zero, a cyclic quadrilateral converges into a cyclic triangle (all triangles are cyclic), and Brahmagupta's formula simplifies to Heron's formula.

3. Shoelace formula - Wikipedia

   en.wikipedia.org/wiki/Shoelace_formula

   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]

4. Heron's formula - Wikipedia

   en.wikipedia.org/wiki/Heron's_formula

   Cyclic Quadrilateral. Heron's formula is a special case of Brahmagupta's formula for the area of a cyclic quadrilateral. Heron's formula and Brahmagupta's formula are both special cases of Bretschneider's formula for the area of a quadrilateral. Heron's formula can be obtained from Brahmagupta's formula or Bretschneider's formula by setting one ...

5. Bretschneider's formula - Wikipedia

   en.wikipedia.org/wiki/Bretschneider's_formula

   Bretschneider's formula generalizes Brahmagupta's formula for the area of a cyclic quadrilateral, which in turn generalizes Heron's formula for the area of a triangle.. The trigonometric adjustment in Bretschneider's formula for non-cyclicality of the quadrilateral can be rewritten non-trigonometrically in terms of the sides and the diagonals e and f to give [2] [3]

6. Quadrilateral - Wikipedia

   en.wikipedia.org/wiki/Quadrilateral

   The quadrilateral with given side lengths that has the maximum area is the cyclic quadrilateral. [43] Of all convex quadrilaterals with given diagonals, the orthodiagonal quadrilateral has the largest area. [38]: p.119 This is a direct consequence of the fact that the area of a convex quadrilateral satisfies

7. Which 38 Republicans voted against Trump's plan to keep the ...

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   The U.S Capitol is seen after U.S, President-elect Donald Trump called on U.S. lawmakers to reject a stopgap bill to keep the government funded past Friday, raising the likelihood of a partial ...

8. Cyclic quadrilateral - Wikipedia

   en.wikipedia.org/wiki/Cyclic_quadrilateral

   Other names for these quadrilaterals are concyclic quadrilateral and chordal quadrilateral, the latter since the sides of the quadrilateral are chords of the circumcircle. Usually the quadrilateral is assumed to be convex, but there are also crossed cyclic quadrilaterals. The formulas and properties given below are valid in the convex case.

9. Joe Jonas Reveals the Prank That Led Him to be Airlifted to a ...

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   Joe Jonas is opening up about a scary incident that happened while on tour that resulted in him needing 67 stitches.. The musician shared the story of how he and his brothers were filming a ...