Question

find the area of a quadrilateral whose vertices are (3,5),(6,6),(4,3)and (1,2)​

Answer 1

Step-by-step explanation:

Area of a quadrilateralABCD=Area of △ABD+Area of △BCD

Area of a triangle=

2

1

∣

∣

∣

∣

∣

∣

∣

∣

x

1

x

2

x

3

y

1

y

2

y

3

1

1

1

∣

∣

∣

∣

∣

∣

∣

∣

Area of a △ABD=

2

1

∣

∣

∣

∣

∣

∣

∣

∣

−3

−5

1

4

−6

2

1

1

1

∣

∣

∣

∣

∣

∣

∣

∣

=

2

1

[−3(−6−2)−4(−5−1)+1(−10+6)]

=

2

1

[24+24−4]=

2

44

=22

Area of a △BCD=

2

1

∣

∣

∣

∣

∣

∣

∣

∣

−5

4

1

−6

−1

2

1

1

1

∣

∣

∣

∣

∣

∣

∣

∣

=

2

1

[−5(−1−2)+6(4−1)+1(8+1)]

=

2

1

[15+18+9]=

2

42

=21

∴ Area of a quadrilateralABCD=Area of △ABD+Area of △BCD=22+21=43sq.units.