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Question

Find the area of the quadrilateral whose vertices, taken in order, are (-4,-2),(-3,-5),(3,-2) and (2,3) .


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Solution

Find the area of given quadrilateral

Given vertices are A(-4,-2),B(-3,-5),C(3,-2)&D(2,3)


If the vertices of quadrilateral is given as A(x1,y1),B(x2,y2),A(x3,y3)&D(x4,y4)
then area of quadrilateral =12(x1y2+x2y3+x3y4+x4y1)-(x2y1+x3y2+x4y3+x1y4)
Area of given quadrilateral

=12((-4)(-5)+(-3)(-2)+(3)(3)+2(-2))-((-3)(-2)+(3)(-5)+(2)(-2)+(-4)(3))
=12(20+6+9-4)-(6-15-4-12)=12×(31+27)=28sq.unit

Hence the required area is 28sq.unit


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