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Coolidge's formula (area of a general convex quadrilateral)

A quadrilateral is a polygon with four sides (or edges) and four vertices or corners. Coolidge’s formula calculates the area of a general convex ... more

Cyclic quadrilateral (tangent of the acute angle between the diagonals)

In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle. This circle is ... more

Cyclic quadrilateral (Ptolemy's theorem)

In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle. This circle is ... more

Area of a convex quadrilateral (in terms of sides and angle θ of the diagonals)

Quadrilateral is a polygon with four sides (or edges) and four vertices or corners. The area of a quadrilateral can be calculated by the sides and the ... more

Cyclic quadrilateral (Length of the diagonal opposite angle A)

In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle. This circle is ... more

Cyclic quadrilateral (Length of the diagonal opposite angle B)

In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle. This circle is ... more

Area of a convex quadrilateral (in trigonometric terms)

Quadrilateral is a polygon with four sides (or edges) and four vertices or corners. The area of a convex quadrilateral can be expressed in trigonometric ... more

Trapezoid ( distance between the midpoints of the diagonals)

Trapezoid is a convex quadrilateral with only one pair of parallel sides. The parallel sides are called the bases of the trapezoid and the other two sides ... more

Orthodiagonal quadrilateral (the sum of the squares of two opposite sides)

In Euclidean geometry, an orthodiagonal quadrilateral is a quadrilateral in which the diagonals cross at right angles. It is a four-sided figure in which ... more

Product of the diagonals in a convex quadrilateral(Bretschneider's formula for diagonals)

A quadrilateral is a polygon with four sides (or edges) and four vertices or corners. In any convex quadrilateral ABCD, the ... more

Bretschneider's formula - Area of a general quadrilateral

In geometry, Bretschneider’s formula is the shown expression for the area of a general quadrilateral.

A quadrilateral is a polygon with four ... more

Euler's quadrilateral theorem

In any convex quadrilateral the sum of the squares of the four sides is equal to the sum of the squares of the two diagonals plus four times the square of ... more

Quadrilateral's length of the diagonals

A quadrilateral is a polygon with four sides (or edges) and four vertices or corners. The interior angles of a simple (and planar) quadrilateral add up to ... more

Brahmagupta's formula (area of a cyclic quadrilateral )

In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle. This circle is ... more

Orthodiagonal quadrilateral (medians of the four triangles)

A quadrilateral is a polygon with four sides (or edges) and four vertices or corners. An orthodiagonal quadrilateral is a quadrilateral in which the ... more

Orthodiagonal quadrilateral (altitudes of the four triangles)

A quadrilateral is a polygon with four sides (or edges) and four vertices or corners. An orthodiagonal quadrilateral is a quadrilateral in which the ... more

Orthodiagonal quadrilateral ( circumradii of the four triangles)

A quadrilateral is a polygon with four sides (or edges) and four vertices or corners. An orthodiagonal quadrilateral is a quadrilateral in which the ... more

Cyclic quadrilateral (sine of an angle)

In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle. This circle is ... more

Cyclic quadrilateral (tangent of an angle)

In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle. This circle is ... more

Cyclic quadrilateral (cosine of an angle)

In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle. This circle is ... more

Cyclic quadrilateral circumradius ( Parameshvara's formula )

In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle. This circle is ... more

Area of rhombus (by diagonals)

Rhombus is a simple (non-self-intersecting) quadrilateral whose four sides all have the same length. Every rhombus is a parallelogram, and a rhombus with ... more

Area of a convex quadrilateral (in terms of the sides and angles)

A quadrilateral is a polygon with four sides (or edges) and four vertices or corners.The area of a convex quadrilateral can be expressed in terms of the ... more

Tangential quadrilateral ( the sum of the opposite sides)

In Euclidean geometry, a tangential quadrilateral (sometimes just tangent quadrilateral) or circumscribed quadrilateral is a convex quadrilateral whose ... more

Varignon's theorem (Varignon parallelogram)

The Varigons theorem states that :
The midpoints of the sides of an arbitrary quadrangle form a parallelogram. If the quadrangle is convex or ... more

Perimeter of Rectangle

A rectangle is any quadrilateral with four right angles. A convex quadrilateral is a rectangle if and only if it is any one of the following:
an ... more

Parallelogram area ( diagonals' angle)

Parallelogram is a simple (non self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of ... more

Rhombus area (trigonometric function)

A rhombus (◊), plural rhombi or rhombuses, is a simple (non-self-intersecting) quadrilateral all of whose four sides have the same length. Another name is ... more

Height of a trapezoid in relation with the sides

Trapezoid is a convex quadrilateral with only one pair of parallel sides. The parallel sides are called the bases of the trapezoid and the other two sides ... more

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