Question

If A(-5, 7), B(-4, -5), C(-1, -6) andD(4, 5) are the vertices of a quadrilateral. Then, find the area of the quadrilateral ABCD.​

Answer 1

Answer:

A(-5,7)

B(-4,-5)

C(-1,-6)

D(4,5)

We will cut the quadrilateral into two triangles

i.e.TriangleABD and TriangleBCD

Now Ar(ABD)

A(-5,7),B(-4,-5),D(4,5)

Ar=1/2[x1(y2-y3)+x2(y3-y1)+x3(y1-y2)]

=1/2[-5(-5-5)+(-4)(5-7)+4(7-(-5)]

=1/2[50+(-27)+33]

=1/2[56]

=56/2

=28

Now Ar(BCD)

B(-4,-5),C(-1,-6),D(4,5)

Ar=1/2[x1(y2-y3)+x2(y3-y1)+x3(y1-y2)]

=1/2[-4(-6-5)+(-1)(5-(-5))+4(-5-(-6)]

=1/2[44+0+4)

=1/2[44+4]

=1/2[48]

=48/2

=24

Now adding Ar(ABD)+Ar(BCD)

=28+24

=52sq.units

Hope it had helped you!!!!