Q. 634.2( 5 Votes )

If P (-5, -

Answer :

Let P(−5,−3); Q(−4,−6); R(2,−3) and S(1,2) be the vertices of quadrilateral PQRS.


Area of the quadrilateral PQRS = Area of ∆PQR + Area of ∆PSR


Area of the triangle having vertices (x1,y1), (x2,y2) and (x3,y3)


= |x1(y2-y3)+x2(y3-y1)+x3(y1-y2)|


Area of ∆PQR = |− 5( − 6 + 3 ) − 4( − 3 + 3 ) + 2( −3 + 6) |


= |15 + 0 + 6|


= sq. units


Area of ∆PSR = | − 5( 2 + 3 ) + 1( − 3 + 3 ) + 2( − 3 2) |


= | − 25 + 0 10 |


= sq. units


Area of the quadrilateral PQRS = + = 28 sq. units


Hence, the area of the quadrilateral is 28 sq. units.


(given answer is wrong, its not 13, it is 28 )

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