Suchergebnisse
Suchergebnisse:
The four maltitudes of a convex quadrilateral are the perpendiculars to a side—through the midpoint of the opposite side. Area of a convex quadrilateral. There are various general formulas for the area K of a convex quadrilateral ABCD with sides a = AB, b = BC, c = CD and d = DA. Trigonometric formulas
- Tangential quadrilateral
In Euclidean geometry, a tangential quadrilateral (sometimes...
- Cyclic quadrilateral
A convex quadrilateral ABCD is cyclic if and only if an...
- Bicentric quadrilateral
Bicentric quadrilateral. In Euclidean geometry, a bicentric...
- Tangential quadrilateral
The area K of an orthodiagonal quadrilateral equals one half the product of the lengths of the diagonals p and q: =. Conversely, any convex quadrilateral where the area can be calculated with this formula must be orthodiagonal.
History. The Shape of Convex Quadrilateral. Some Common Convex Quadrilateral. Properties of a Convex Quadrilateral. Area of a Convex Quadrilateral. Using Diagonals. Bretschneider’s Formula. Using Sides and Angles. Using Sides and Only One Angle. Using Only Sides and Diagonals. Using Diagonals as Vectors. Lengths of Diagonals. Angular Bisectors.
1. Let $a,b,c,d$ be the four sides of the quadrilater, and let $p= \frac {a+b+c+d} {2}$. Then the area $S$ is given by. $$S^2= (p-a) (p-b) (p-c) (p-d)-abcd \cos^2 (\frac {A+C} {2})$$. So, the four sides together with the sum of the angles $A,C$ uniquely determine the area.
