Question

if A(-4,-2) B(-3,-5) C(3,-2) D(2,3) are the vertices of quadrilateral ABCD find the area of quadrilateral using coordinate geometry lesson formula​

Answer 1

Hope it helps u........

Answer 2

Area of Quadrilateral is 28 $unit^2$

Step-by-step explanation:

• Let A (–4, –2), B (–3, –5), C(3, –2) and D(2, 3) be the vertices of the quadrilateral.              

• Let us join diagonal BD.

Now, ar(ΔABD) = $\frac {1}{2} [(-4)(-5-3) + (-3)(3-(-2))+ (2)((-2)-(-5))]$

= $\frac {1}{2}[(-4)(-8) + (-3)(5) + 2(-2+5)]$

= $\frac {1}{2}[32+(-15)+6]$

= $\frac {1}{2} [23]$

= 11.5 $unit^2$

ar(ΔBCD) = $\frac {1}{2}\times [(3)(-5-3) + (-3)(3-(-2))+ (2)((-2)-(-5))]$

= $\frac {1}{2}[(3)(-8) + (-3)(5) + 2(3)]$

= $\frac {1}{2}[-24+(-15)+6]$

= $\frac {1}{2} (-33)$

= 16.5 $unit^2$

Since, ar(quad ABCD) = ar(ΔABD)+ ar(ΔBCD)

ar(quad ABCD) = 11.5 + 16.5

= 28 $units^2$