Area of Parallelogram in Terms of Its Diagonals

angle

a

b

double

translate

The area

A

of a parallelogram (shown in blue) with sides

a

and

b

is



a

×

b



. This Demonstration shows that double the area is

2A=

e

×



f



, where

e

and

f

are the diagonals. So the area of a parallelogram can be expressed in terms of its diagonals

e

and

f

as well as its sides.