Quadrilateral: Area Of A Convex Quadrilateral
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Area Of A Convex Quadrilateral
The 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.
The 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:
If 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.
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