Question

find the area of quadrilateral whose vertices are (1,1),(3,4),(5,-2) and (4,-7)?​

Answer 1

Answer:

Let the points be A(1,2),B(6,2),C(5,3) and D(3,4)

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

(1)(2−3)+(6)(3−2)+5(2−2)

∣

∣

∣

∣

=

∣

∣

∣

2

−1+6

∣

∣

∣

=

2

5

squnits

And, Area of triangle ACD =

∣

∣

∣

∣

2

(1)(3−4)+(5)(4−2)+3(2−3)

∣

∣

∣

∣

=

∣

∣

∣

2

−1+10−3

∣

∣

∣

=

2

6

=3squnits

Hence, Area of quadrilateral =

2

5

+3=

2

11

squnits