Question

If the P Q R S are the vertices of quadrilateral P= ( _5,_3) Q=(_4 ,_6) R = (2,_3) S= ( 1,2) find the its area​

Answer 1

Answer:

he quadrilateral ABCD can be divided into triangles PQS and RSQ 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

)

∣

∣

∣

∣

∣

Area of quadrilateral PQRS = area of triangle PQS + area of triangle RSQ

area of △PQS=

2

1

[−5(−6−2)+(−4)(2+3)+1(−3+6)]

=

2

1

[23]sq. units

area of △RSQ=

2

1

[2(2+6)+1(−6+3)+(−4)(−3−2)]

=

2

1

[33]sq. units

Area of quadrilateral PQRS = area of triangle PQS + area of triangle RSQ

=

2

1

[23]+

2

1

[33]

=

2

56

=28sq.units

solution