Question

Find the area of the quadrilateral ABCD whose vertices are A(-4,-3), B(3, 1), C(0, 5) and D(-4, 2).

Answer 1

Answer:

The coordinates of ABCD are A(−3,−1),B(−2,−4),C(4,−1),D(3,4).

Area of quadrilateral ABCD = Area of triangle ABC + Area of triangle ACD

Area of triangle =

2

1

∣[x

1

(y

2

−y

3

)+x

2

(y

3

−y

1

)+x

3

(y

1

−y

2

)]∣

Area of triangle ABC =

2

1

∣[−3(−4+1)−2(−1+1)+4(−1+4)]∣

=

2

1

∣[9+12]∣=

2

21

sq. units

Area of triangle ACD =

2

1

∣[−3(−1−4)+4(4+1)+3(−1+1)]∣

=

2

1

∣[15+20]∣=

2

35

sq. units

Therefore, Area of quadrilateral ABCD =

2

21

+

2

35

=28 sq. units