Question

Find the area of the quadrilateral ABCD, whose vertices are A(−3, −1), B (−2, −4), C(4, − 1) and D (3, 4).

Answer 1

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