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

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The area of a triangle with vertices (a, b + c), (b, c + a) and (c, a + b) is 0. Explanation: Let the vertices of a triangle are, A ≡ (x1, y1) ≡ (a, b + c) B ≡ (x2, y2) ≡ (b, c + a) and C = (x3, y3) ≡ (c, a + b) ∵ Area of ΔABC = Δ = `$\frac{1}{2}$[x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)] $\therefore$ Δ = $\frac{1}{2}$[a(c + a - a - b) + b(a + b - b - c) + c(b + c - c - a)] = $\frac{1}{2}$[a(c - b) + b(a - c) + c(b - a)] = $\frac{1}{2}$(ac - ab + ab - bc + bc - ac) = $\frac{1}{2}$(0)` = 0 Hence, the required area of triangle is 0.

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