The area of the quadrilateral whose vertices are `(1,2)(6,2),(5,3) and (3,4)`, is

Options

A. `(3)/(2)` sq. unirts
B. `(11)/(2)` sq. unirts
C. `(1)/(2)` sq. unirts
D. none of these

Answer

B

Explanation

We have,
`Delta_(1)(1)/(2)|{:(1,6),(2,2):}|=-5,Delta_(2)=(1)/(2)|{:(6,5),(2,3):}|=4`
`Delta_(3)(1)/(2)|{:(5,3),(3,4):}|=(11)/(5)and Delta_(4)=(1)/(2)|{:(3,1),(4,2):}|=1`
`:.` Area of quadrilateral `=|-5+4+(11)/(4)+1|=(11)/(2)` sq. units