Quadrilateral: Area Of A Convex QuadrilateralRelated Resources : Quadrilateral
Area Of A Convex QuadrilateralTrigonometric FormulasThe area can be expressed in trigonometric terms as pq \cdot \sin \theta, pq since θ is 90°. Another area formula in terms of the sides and angles, with angle C being between sides b and c, and A being between sides a and d, is Alternatively, we can write the area in terms of the sides and the intersection angle θ of the diagonals, so long as this angle is not 90°: \cdot \left a^2 + c^2  b^2  d^2 \right .\tan \theta\cdot \left a^2  b^2 \right. Another area formula including the sides a, b, c, d is where x is the distance between the midpoints of the diagonals and φ is the angle between the bimedians. Nontrigonometric FormulasThe following two formulas expresses the area in terms of the sides a, b, c, d, the semiperimeter s, and the diagonals p, q: The area can also be expressed in terms of the bimedians m, n and the diagonals p, q: Vector FormulasArea InequalitiesIf a convex quadrilateral has the consecutive sides a, b, c, d and the diagonals p, q, then its area K satisfies p^2+q^2 with equality only if the diagonals are perpendicular and equal. with equality only for a rectangle. Related Categories
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