Question

Find the area of the quadrilateral $ABCD$ , the co-ordinates of whose vertices are $A(5,-2),B(-3,-1),C(2,1)$and $D(6,0)$ .

Answer 1

According to the question, Coordinates of the quadrilateral are;

$A(5,-2)=(x_1,y_1)$

$B(-3,-1)=(x_2,y_2)$

$C(2,1)=(x_3,y_3)$

$D(6,0)=(x_4,y_4)$

To find area of quadrilateral we will use the formula,

Area of quadrilateral $ABCD=\frac{1}{2}\left|\right(x_1-x_3\left)\right(y_2-y_4)-(y_1-y_3\left)\right(x_2-x_4\left)\right|$

$=\frac{1}{2}\left|\right(5-2\left)\right(-1-0)-(-2-1\left)\right(-3-6\left)\right|$

$=\frac{1}{2}|3\times (-1)-(-3)\times (-9)|$

$=\frac{1}{2}|-3-27|$

$=\frac{1}{2}\times 30$

$=15$ unit². ..... Answer