Една кратка формула за лице на четириъгълник и нейното приложение
A short formula for the area of a quadrilateral and its application

Summary/Abstract: A formula is derived for the area of a convex quadrilateral including its sides and diagonals. It generalized Brahmagupta’s formula for the area of an inscribed quadrilateral. Also, an important relation is obtained between the sides and the diagonals of an arbitrary quadrilateral. It helps to determine the area of a convex quadrilateral using three of its sides and the diagonals only. The derived formula is applied for some inequalities between the sides and the diagonals of a convex quadrilateral, while the obtained relation – to determine the diagonals of a convex pentagon when two of them and its sides are known.

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