Question

Find the area of the quadrilateral $ABCD$, whose vertices are $A(1,0),B(5,3),C(2,7)$ and $D(-2,4)$.

Answer 1

Area of a quadrilateral$=\frac{1}{2}[(x_1{y}_2+x_2{y}_3+x_3{y}_4+x_4{y}_1)-(x_2{y}_1+x_3{y}_2+x_4{y}_3+x_1{y}_4)]$

$x_1=1,x_2=5,x_3=2,x_4=-2,y_1=0,y_2=3,y_3=7$ and $y_4=4$

Area of a quadrilateral$=\frac{1}{2}[(1\times 3+5\times 7+2\times 4-2\times 0)-(5\times 0+2\times 3-2\times 7+1\times 4)]$

$=\frac{1}{2}[(3+35+8-0)-(0+6-14+4)]$

$=\frac{1}{2}[46+4]=25$sq.units