Given that, the coordinates of the vertices of a triangle are (1, −1), (−4, 6), (−3, −5)
Let us Assume A(x1, y1) = (1, −1), B(x2, y2) = (−4, 6) and C(x3, y3) = (−3, −5)
We know that,
Area of triangle = 1/2 [x1(y2 − y3) + x2(y3 − y1) + x3(y1 − y2)]
Therefore,
Area of the given triangle = 1/2 [{1(6 − (−5))} + {(−4) (−5 − (−1))} + {(−3) ((−1) −6)}]
⇒ 1/2 {11 + 16 + 21}
⇒ 48/2 = 24 square units
Hence, the area of the triangle with given vertices is 24 square units.
