Write the area of the triangle having vertices at `(a , b+c),\ (b , c+a),\ (c , a+b)dot`

Explanation

Let `A(a, b+c), B(b, c+a)` and` C(c, a+b)` be the vertices of the the given triangle.


Area of triangle `ABC=frac{1}{2}|x_{1}(y_{2}-y_{3})+x_{2}(y_{3}-y_{1})+x_{3}(y_{1}-y_{2})| `

`=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}|a c-a b+a b-b c+b c-a c| `

`=0`


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