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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).
[CBSE 2015]

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Solution

By joining P and R, we get two triangles PQR and PRS.
Let Px1, y1=P-5, -3, Qx2, y2=Q-4, -6, Rx3, y3=R2, -3 and Sx4, y4=S1, 2. Then
Area of PQR=12x1y2-y3+x2y3-y1+x3y1-y2 =12-5-6+3-4-3+3+2-3+6 =1215-0+6=212 sq. units
Area of PRS=12x1y3-y4+x3y4-y1+x4y1-y3 =12-5-3-2+22+3+1-3+3 =1225+10+0=352 sq. units
So, the area of the quadrilateral PQRS is 212+352=28 sq. units sq. units.

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