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Quadrilateral: Area Of A Convex Quadrilateral


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Area Of A Convex Quadrilateral

Trigonometric Formulas

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, 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.

Non-trigonometric Formulas

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.

Vector Formulas


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