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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.

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To find the area of the quadrilateral ABCD with vertices A(-5, 7), B(-4, -5), C(-1, -6), and D(4, 5), we can divide the quadrilateral into two triangles: ABC and ACD. We will then calculate the area of each triangle using the formula for the area of a triangle given by its vertices. ### Step 1: Calculate the area of triangle ABC The formula for the area of a triangle given vertices (x1, y1), (x2, y2), (x3, y3) is: \[ \text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right| ...
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