Step-by-step explanation:
The given four sides of quadrilateral = (2, 4), (3, 5), (4, 6) and (5,8)
To find, the area of the quadrilateral = ?
We know that,
The area of quadrilateral [tex]=\dfrac{1}{2} [x_{1}( y_{2}-y_{3})+x_{2}( y_{3}-y_{4})+x_{3}( y_{4}-y_{1})+x_{4}( y_{1}-y_{2})][/tex]
[tex]=\dfrac{1}{2} [2( 5-6)+3( 6-8)+4( 8-4)+5(4-5)][/tex]
[tex]=\dfrac{1}{2} [2(-1)+3(-2)+4(4)+5(-1)][/tex]
[tex]=\dfrac{1}{2} (-2-6+16-5)[/tex]
[tex]=\dfrac{1}{2} (16-13)[/tex]
= [tex]\dfrac{3}{2}[/tex] units
Thus, the area of the quadrilateral is [tex]\dfrac{3}{2}[/tex] units.
