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°.
The area can be also expressed in terms of bimedians as
where the lengths of the bimedians are m and n and the angle between them is φ.
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, isAlternatively, 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 the lengths of two diagonals and one bimedian are given.
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