If A(−4, 8), B(−3, −4), C(0, −5) and D(5, 6) are the vertices of a quadrilateral ABCD, find its area. - Mathematics

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If A(−4, 8), B(−3, −4), C(0, −5) and D(5, 6) are the vertices of a quadrilateral ABCD, find its area.

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Solution

Let the vertices of the quadrilateral be A(−4, 8), B(−3, −4), C(0, −5) and D(5, 6).

Join AC to form two triangles, namely, ΔABC and ΔACD.

Area of quadrilateral ABCD = Area of ΔABC + Area of ΔACD

We know

Area of triangle having vertices (x1, y1), (x2, y2) and (x3, y3) =`1/2`[x1(y2y3)+x2(y3y1)+x3(y1y2)]

Now,

Area of ABC=`1/2`{(4)[(4)(5)]+(3)[(5)(8)]+(0)[(8)(4)]}

=`1/2`(4+39)

`=35/2 `

Area of ACD=`1/2`{(4)[(5)(6)]+(0)[(6)(8)]+(5)[(8)(5)]}

=`1/2`(44+65)

`=109/2`

Area of quadrilateral ABCD=Area of ABC+Area of ACD

`35/2+109/2`

=72 square units

Thus, the area of quadrilateral ABCD is 72 square units.

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2014-2015 (March) Delhi Set 1

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