The area of a triangle with vertices (a, b + c), (b, c + a) and (c, a + b) is

Let the vertices of a triangle = A, B and C

Where;

A = (x_{1}, y_{1}) = (a, b + c)

B = (x_{2}, y_{2}) = (b, c + a) and

C = (x_{3}, y_{3}) = (c, a + b)

∵ Area of

[x_{1}(y_{2} – y_{3}) + x_{2}(y_{3} – y_{1}) + x_{3}(y_{1} – y_{2})]

[a(c - b) + b(a - c) + c(b - a)]

[ac - ab + ab - bc + bc - ac] = (0) = 0

Hence, the area of triangle is 0.

18