If A(-3,5) ,B (-2,-7) ,C(1,-8) and D(6,3) are the vertices of a quadrilateral ABCD find its area.
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Solution
In triangle ABD, Area of triangle =1/2[-3(-7-3)-2(3-5)+6(5+7) = 1/2 [-3×-10 -2×-2 +6×12] =1/2 × 30 +4 +72 =1/2×106 =53cm in triangle BCD area of triangle =1/2 [-2(-8-3)+1(3+7)+6(-7+8) =1/2[-2×-11 +10+6] =1/2×22+10+6 =1/2×38 =19 cm
so,area of quadilateral=area of triangle ABD+area of triangle BCD =53+19 = 72 cm²