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The area of quadrilateral, the coordinates of whose angular points taken in order are (1,1),(3,4),(5,−2) and (4,−7) is ____.

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Detailed Solution

On illustrating the points, we get:

The quadrilateral ABCD is divided into triangles ABC and ADC.
Area of quadrilateral = Area of ABC + Area of ADC.
We know, area of triangle with vertices

Area of ABC:
Question Image

Similarly,
Area of ADC Question Image

Area of ADC

Total area of quadrilateral ABCD is:

The area of quadrilateral, the coordinates of whose angular points taken in order are (1,1),(3,4),(5,−2) and (4,−7)

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