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प्रश्न
Find the area of the quadrilateral ABCD, whose vertices are A(−3, −1), B (−2, −4), C(4, − 1) and D (3, 4).
उत्तर
The given quadrilateral i.e., ABCD whose vertices are A (−3, −1), B (−2, −4), C (4, −1) and D (3, 4) can be drawn as follows:
Here, B is joined with D.
We know that the area of a triangle whose vertices are (x1 , y1 ), (x2 , y2 ) and (x3 , y3 ) is given by
`=1/2[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]`
`=1/2[-3(-8)-2(5)+3(3)]`
`=1/2[24-10+9]`
`=23/2`
`=11.5 sq.inits`
∴ar(ΔABD)
`=1/2[-3(-4-4)+(-2)(4+1)+3(-1+4)]`
∴ar (ΔCDB)
`=1/2[4(4+4)+3(-4+1)+(-2)(-1-4)]`
`=1/2[(4xx8)+(3x-3)-2xx(-5)]`
`=1/2[32-9+10]`
`=33/2`
`=16.5 sp.unit`
Thus, ar (ABCD) = ar (ΔABD) + ar (ΔCDB) = (11.5 + 16.5) sq units = 28 sq units
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