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Question
Find the area of quadrilateral PQRS whose vertices are P(-5, -3), Q(-4,-6),R(2, -3) and S(1,2).
Solution
By joining P and R, we get two triangles PQR and PRS.
`"let" P (x_1, y_1) = P (-5,-3) , Q(x_2,y_2) = Q(-4,-6), R (x_3,y_3) = R(2,-3) and . Then S(x_4,y_4) = S(1,2)`
`"Area of " ΔPQR = 1/2 [ x_1 (y_2-y_3) +x_2(y_3-y_1)+x_3 (y_1-y_2)]`
`=1/2 [-5(-6+3)-4(-3+3)+2(-3+6)}`
`=1/2 [15-0+6]=21/2 sq. units`
`"Area of "Δ PRS = 1/2 [ x_1(y_3-y_4) +x_3 (y_4-y_1)+x_4(y_1-y_3)]`
`=1/2[-5(-3-2)+2(2+3)+1(-3+3)]`
`=1/2[25+10+0]=35/2 sq. units`
So, the area of the quadrilateral PQRS is `21/2+35/2=28 ` sq. units
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