Find the area of quadrilateral PQRS whose vertices are P(–5, –3), Q(–4, – 6), R(2, –3) and S(1, 2).
For triangle PQR
Area of triangle
= l1/2(x1(y2−y3) + x2(y3−y1) + x3(y1−y2))l
= 1/2(–5(–6 + 3)–4(–3 + 3) + 2(–3 + 6))
= 1/2(15 + 0 + 6)
= 1/2(21)
For triangle PRS
Area of triangle
= 1/2(x1(y2−y3) + x2(y3−y1) + x3(y1−y2))
= 1/2(–5(–3–2) + 2(2–(–3)) + 1(–3 + 3))
= 1/2(25 + 10 + 0)
= 1/2(35)
Area of ABCD = Area of ABC + Area of ACD
= 21/2 + 35/ 2
= 28 sq units