Question

find the area of quadratic those vertical or (- 3 - 4) (- 5 - 6) (4 - 1) and (1,2)​

Answer 1

Step-by-step explanation:

ANSWER

Let the points be A(−3,2),B(5,4),C(7,−6) and D(−5,−4)

The quadrilateral ABCD can be divided into triangles ABC and ACD and hence the area of the quadrilateral is the sum of the areas of the two triangles.

Area of a triangle with vertices (x

1

,y

1

) ; (x

2

,y

2

) and (x

3

,y

3

) is

∣

∣

∣

∣

∣

2

x

1

(y

2

−y

3

)+x

2

(y

3

−y

1

)+x

3

(y

1

−y

2

)

∣

∣

∣

∣

∣

Hence, Area of triangle ABC

=

∣

∣

∣

∣

∣

2

(−3)(4+6)+(5)(−6−2)+(7)(2−4

∣

∣

∣

∣

∣

=

∣

∣

∣

∣

∣

2

−30−40−14

∣

∣

∣

∣

∣

=

2

84

=42squnits

And, Area of triangle ACD

=

∣

∣

∣

∣

∣

2

(−3)(−6+4)+(7)(−4−2)+(−5)(2+6)

∣

∣

∣

∣

∣

=

∣

∣

∣

∣

∣

2

6−42−40

∣

∣

∣

∣

∣

=

2

76

=38squnits

Hence, Area of quadrilateral =42+38=80squnits