A quadrilateral whose consecutive sides have the lengths ,
,
,
,
where

(1)

and

(2)

Brahmagupta's trapezium is a cyclic quadrilateral
with perpendicular diagonals.

It has area

(3)

circumradius ,

(4)

and the diagonal lengths

All these values are rational if and are. In particular, if and are Pythagorean
triples , the area , circumdiameter, the lengths of the
diagonals are all integers.

See also Brahmagupta's Formula ,

Brahmagupta's Theorem ,

Cyclic
Quadrilateral ,

Trapezium
This entry contributed by Margherita
Barile

Explore with Wolfram|Alpha
References Eves, H. An Introduction to the History of Mathematics, 3rd ed. New York: Holt, Rinehart
and Winston, 1969. Referenced on Wolfram|Alpha Brahmagupta's Trapezium
Cite this as:
Barile, Margherita . "Brahmagupta's Trapezium." From MathWorld --A Wolfram Web Resource, created by Eric
W. Weisstein . https://mathworld.wolfram.com/BrahmaguptasTrapezium.html

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