Q25 of 47 Page 1

If A (– 3, 5), B (– 2, – 7), C (1, – 8) and D (6, 3) are the vertices of a quadrilateral ABCD, find its area.

Let’s divide the quadrilateral ABCD into 2 triangles ΔABC and ΔACD.

Area of triangle with vertices A (x1, y1), B (x2, y2), C (x3, y3) is given by,


(x1 (y2 – y3) + x2 (y3 – y1) + x3 (y1 – y2))


Area of ΔABC = (– 3 (– 7 + 8) + (– 2) (– 8 – 5) + 1 (5 + 7))


= (– 3 + 26 + 12)


= 17.5 sq. units


Area of ΔACD = (– 3 (– 8 – 3) + 1 (3 – 5) + 6 (5 + 8))


= (33 – 2 + 78)


= 54.5 sq. units


⸫ Area of quadrilateral ABCD = (17.5 + 54.5) = 72 sq. units


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