How do you find the area of a quadrangle?

Answer 1

For the general quadrilateral with sides of lengths a, b, c and d,let s = (a+b+c+d)/2

then area = sqrt[s*(s - a)*(s - b)*(s - c)*(s - d) - a*b*c*d*cos 0.5*(A+C)].

Or if the diagonals are of length p an q and the angle between then is X,

then area = 0.5*p*p*sin(X).

The vertical height can only be used with quadrangles with at least one pair of parallel sides and so is of little use in general.