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If A(-5,7), $B − 4, − 5,$ $C − 1, − 6$ and $D (4, 5)$ are the vertices of a quadrilateral, find the area of the quadrilateral ABCD.

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72sq. units

80sq.units

45sq.units

60sq.units

answer is A.

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Detailed Solution

The given vertices of quadrilateral ABCD, A(-5,7), B(-4,-5), C(-1,-6) and D(4, 5) .
The area of the quadrilateral is found by summing up the area of 2 triangles

Δ A B C

and

Δ D A C

We know that area of a triangle is given by the formula:

= 12 {x 1 (y 2 − y 3) + x 2 (y 3 − y 1) + x 3 (y 1 − y 2)}, w h e r e (x 1, y 1), (x 2, y 2) a n d (x 3, y 3) are the vertices of the triangle .

Area of ΔABC

= 12 {− 5 × 1 + (− 4) × (− 13) − 12} = 12 (− 5 + 52 − 12) = 352 s q . units

Area of ΔDAC

= 12 {4 × 13 + (− 5) × (− 11) − (− 2)} = 12 (52 + 55 + 2) = 1092 s q . units

Area of the Quadrilateral ABCD

= Area of Δ A B C + Area of Δ D A C = (352 + 1092) s q . u n i t s = 1442 s q . units = 72 s q . units

Area of the Quadrilateral ABCD is 72 sq.units.
Hence, the correct option is 1.

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