Answer :

The quadrilateral is divided into two triangles ABC and ACD.

Area of the quadrilateral ABCD = Area of triangle ABC + Area of triangle ACD.

Area of triangle ABC =

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

= 1/2 [-3(-4 + 1) + -2(-1 + 1) + 4(-1 + 4)]

= 1/2 [9 + 0 + 12]

= 21/2 sq. units

Area of triangle ACD =

1/2 [x_{1}(y_{3} – y_{4}) + x_{3}(y_{4} – y_{1}) + x_{4}(y_{1} – y_{3})]

= 1/2 [-3(-1 - 4) + 4(4 + 1) + 3(-1 + 1)]

= 1/2 [15 + 20 + 0]

= 35/2 sq. units

∴ Area of the quadrilateral = (21/2) + (35/2)

= (56/2)

= 28 sq. units

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