area(AOB) = sin(w)*(x*y'-x'*y)/2.

Here A(x,y), B(x',y') are the coordinates of the points with respect to the oblique axes shown, w being the angle of the coordinate axes. Deduce that the same area is expressed through.

area(AOB) = (u'*v-v'*u)/(2*sin(w)).

Here (u,v) are the

In particular, when w = 90 degrees, then sin(w)=1 and the formula gives the area as the determinant of the corresponding column vectors, representing now the cartesian coordinates with respect to these orthogonal axes:

Taking the origin as the third point C of a triangle and denoting the cartesian coordinates with C(c

For a couple of similar formulas, giving the area in barycentrics and trilinears, see the file AreaInBarycentrics.html .

area(P

area(P

area(P

The area of the triangle ABC bounded by the lines (see ThreeLines.html ).

ax+by+c=0, a'x+b'y+c'=0, a''x+b''y+c''=0.

AreaOfPedal.html

BarycentricCoordinates.html

ThreeLines.html

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