Question

{(2,4),(3,5),(4,6),(5,8)}

Answer 1

The area of the quadrilateral is $\dfrac{3}{2}$ units.

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 $=\dfrac{1}{2} [x_{1}( y_{2}-y_{3})+x_{2}( y_{3}-y_{4})+x_{3}( y_{4}-y_{1})+x_{4}( y_{1}-y_{2})]$

$=\dfrac{1}{2} [2( 5-6)+3( 6-8)+4( 8-4)+5(4-5)]$

$=\dfrac{1}{2} [2(-1)+3(-2)+4(4)+5(-1)]$

$=\dfrac{1}{2} (-2-6+16-5)$

$=\dfrac{1}{2} (16-13)$

= $\dfrac{3}{2}$ units

Thus, the area of the quadrilateral is $\dfrac{3}{2}$ units.