Parallelogram Parallelogram In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. The congruence of opposite sides and opposite angles is a direct consequence of the Euclidean parallel postulate and neither condition can be proven without appealing to the Euclidean parallel postulate or one of its equivalent formulations. By comparison, a quadrilateral with just one pair of parallel sides is a trapezoid in American English or a trapezium in British English. The
Quadrilateral used for the area of a concave quadrilateral (having the concave part opposite to angle "α") just changing the first sign + to - . The following two formulas express the area in terms of the sides "a", "b", "c", "d", the semiperimeter "s", and the diagonals "p", "q": The first reduces to Brahmagupta's formula in the cyclic quadrilateral case, since then "pq" = "ac" + "bd". The area can also be expressed in terms of the bimedians "m", "n" and the diagonals "p", "q": In fact, any three of the four values "m", "n", "p", and "q" suffice for