Question

Find the area of the quadrilateral PQRS given the vertices P(2,1) , Q(4,2) , R(5,4) , S(3,3)

PLZ ITS URGENT 2MORROW EXAM

Answer 1

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Answer 2

Area of quadrilateral PQRS = 3 sq units

Step-by-step explanation:

Given:

The vertices of the quadrilateral PQRS are P(2,1) , Q(4,2) , R(5,4) , S(3,3).

Area of quadrilateral PQRS = area of triangle [PQR+PSR]

$Area of triangle PQR=\frac{1}{2}[ 2(2-4) + 4(4-1)+5(1-2)] }$

                                         =$\frac{1}{2} (-4+12-5)$

                                         =$\frac{1}{2} (-4+12-5)$

      Area of triangle PQR =1.5 sq.units

Also,

$Area of triangle PSR=\frac{1}{2} [ 2(3-4) + 3(4-1)+5(1-3)] }$

                                 =$\frac{1}{2} (-2+9-10)$

                                 =$\frac{1}{2} (-3)$

                                 = $\frac{-3}{2}$

Area of triangle PSR =-1.5sq.units    

Therefore,    

Area of quadrilateral PQRS= 1.5 + 1.5

                                            = 3 sq units