Name the quadrilateral, ANDY if A(-1, 4), N(2,6), D((5, 4) and Y(2, 2)!

Formula:

Area of quadrilateral = area of triangle 1 + area of triangle 2

Area of triangle =
2
1
​
[x
1
​
(y
2
​
−y
3
​
)+x
2
​
(y
3
​
−y
1
​
)+x
3
​
(y
1
​
−y
2
​
)]

Given,

A(1,2),B(−5,6),C(7,−4),D(k,−2)

Let the first triangle be, ABC

Area of △ABC=
2
1
​
[1(6−(−4))−5(−4−2)+7(2−6)]

=
2
1
​
[10+30−28]

=6sq.units

Area of △ACD=
2
1
​
[1(−4+2)+7(−2−2)+k(2+4)]

=
2
1
​
[−2−28+6k]

=−15+3ksq.units

Area of quadrilateral =6−15+3k=0

k=3