Question

the area of the quadrilateral whose vertices are (1,2),(6,2),(5,3) and (3,7)

Answer 1

A(1,2) B(6,2) C(5,3) D(3,7)

Area of the triangle ABC=1/2|1(2-3)+6(3-2)+5(2-2)

=1/2|1(-1)+6(1)+5(0)

=1/2|-1+6+0|

=1/2|5|

=2.5



Area of triangle ACD= 1/2|1(3-7)+5(7-2)+3(2-3)|

=1/2|1(-4)+5(5)+3(-1)|


=1/2|-4+25-3|

=1/2|18|

=9

Area of quadrilateral =area of ABC + area of the ACD

= 2.5+9

= 11.5