Question

The area of the quadrilateral with vertices at $(4,3),(2,-1),(-1,2),(-3,-2)$ is

• A. $29sq.unit$
• B. $369sq.unit$
• C. $54sq.unit$
• D. $noneofthese$

Answer 1

The correct option is D $noneofthese$

Given $A(4,3)B(+3,-1)C(-1,2)D(-3,-2)$

There are $2△S$

$△ACD$ and $△ABC$

Area of $ABCD=$ area of $△ABC+$ area of $△ACD$

$=\frac{1}{2}\left[4\right(-1-2)+2(2-3)+-1(3-(-1)\left)\right]$

$+\frac{1}{2}\left[4\right(2-(-2))-1(-2-3)-3(3-2\left)\right]$

$=\frac{1}{2}[-12-2-4]+\frac{1}{2}[16+5-3]$

$=\frac{1}{2}[-18+21-3]=0$