Question

Find the area of the quadrilateral whose vertices are W(1,4) X(4,8) Y(8,5) Z(5,2)
[please tell the correct answer]​

Answer 1

Step-by-step explanation:

Consider the given vertices.

A(6,9),B(7,4),C(4,2) and D(3,7)

We know that area of the quadrilateral

=

2

1

×[(x

1

y

2

+x

2

y

3

+x

3

y

4

+x

4

y

1

)−(x

2

y

1

+x

3

y

2

+x

4

y

3

+x

1

y

4

)]

where (x

1

,y

1

),(x

2

,y

2

),(x

3

,y

3

),(x

4

,y

4

) are the vertices of quadrilateral

So, the area of the quadrilateral ABCD

=

2

1

×∣((6)(4)+(7)(2)+(4)(7)+(3)(9))−((7)(9)+(4)(4)+(3)(2)+(6)(7))∣

=

2

1

×∣(24+14+28+27)−(63+16+6+42)∣

=

2

1

×∣93−127∣

=

2

1

×∣−34∣

=

2

1

×34=17 units

2

Hence, this is the answer.