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If A(-5,\ 7),\ B(-4,\ -5),\ C(-1,\ -6)\ ...

If `A(-5,\ 7),\ B(-4,\ -5),\ C(-1,\ -6)\ a n d\ D(4,\ 5)`are the vertices of a quadrilateral, find the area of the quadrilateral ABCD.

Text Solution

Verified by Experts

The quadrilateral can be formed into two triangles, by joining A to C
thus area of quadrilateral = area of triangles ABC and ADC
Area of triangle with three vertices (a,b), (c,d) and (e,f) is given as,
`Area = 1/2[a(d-f)+c(f-b)+e(b-d)]`
Now, area of triangle ABC
Thus, the coordinates are `(-5,7), (-4,-5) and (-1,-6)`
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