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The area K of an orthodiagonal quadrilateral equals one half the product of the lengths of the diagonals p and q: [8] K = p q 2 . {\displaystyle K={\frac {pq}{2}}.} Conversely, any convex quadrilateral where the area can be calculated with this formula must be orthodiagonal. [ 6 ]
A tangential quadrilateral with its incircle. In Euclidean geometry, a tangential quadrilateral (sometimes just tangent quadrilateral) or circumscribed quadrilateral is a convex quadrilateral whose sides all can be tangent to a single circle within the quadrilateral.
In the case of an orthodiagonal quadrilateral (e.g. rhombus, square, and kite), this formula reduces to = since θ is 90°. The area can be also expressed in terms of bimedians as [16] = , where the lengths of the bimedians are m and n and the angle between them is φ.
A formula for the area K of a cyclic orthodiagonal quadrilateral in terms of the four sides is obtained directly when combining Ptolemy's theorem and the formula for the area of an orthodiagonal quadrilateral. The result is [29]: p.222 = (+).
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Alternatively, the area can be calculated by dividing the kite into two congruent triangles and applying the SAS formula for their area. If a {\displaystyle a} and b {\displaystyle b} are the lengths of two sides of the kite, and θ {\displaystyle \theta } is the angle between, then the area is [ 27 ] A = a b ⋅ sin θ . {\displaystyle ...
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