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Question

If A(-3,5) ,B (-2,-7) ,C(1,-8) and D(6,3) are the vertices of a quadrilateral ABCD find its area.


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

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