Question

What is the area of the quadrilateral whose angular points are: (2, 4), (3, 2), (8, 4), (7, 6)?​

Answer 1

Answer:

Given: vertices of the quadrilateral be A(1,2),B(−5,6),C(7,−4) and D(h,−2).

Let join AC to form two triangles,

Now, We know that

Area of triangle =

2

1

[x

1

(y

2

−y

3

)+x

2

(y

3

−y

1

)+x

3

(y

1

−y

2

)]

Then,

Area of triangle ABC =

2

1

[1(6+4)−5(−4−2)+7(2−6)]

=

2

1

[10+30−28]

=

2

12

=6 sq units

Now, Area of triangle ADC

=

2

1

[1(−2+4)+h(−4−2)+7(2+2)]

=

2

1

[2−6h+28]

=

2

12

[−6h+30]

=3h−15

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

=3h−15+6

=3h=9

=h=3

Hence, h is 3.