Q31 of 47 Page 1

If are the vertices of a quadrilateral PQRS, find its area.

To find the area of the quadrilateral PQRS, we divide the quadrilateral into two triangles by joining P and R.


So Area(PQRS)=Area(ΔPQR) + Area(ΔPRS)


Now,


Area(ΔPQR)=[x1(y2-y3) + x2(y3-y1) + x3(y1-y2)]


=[(-5)(-6-(-3)) + (-4)(-3-(-3)) + 2(-3-(-6))]


=[(-5) × (-3) + 0 + 2(3)]=21/2=10.5sq. units


Area(ΔPRS)=[x1(y2-y3) + x2(y3-y1) + x3(y1-y2)]


=[(-5)(-3-2) + 2(2-(-3)) + 1(-3-(-3))]


=[25 + 10 + 0]


=[35]=17.5 sq. units


Area(PQRS)=Area(ΔPQR) + Area(ΔPRS)


⇒ Area(PQRS)=10.5 + 17.5=28sq.units


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