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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.                          [CBSE 2014]


Solution

It is given that A(−3, 5), B(−2, −7), C(1, −8) and D(6, 3) are the vertices of a quadrilateral ABCD.



Area of the quadrilateral ABCD = Area of ∆ABC + Area of ∆ACD

arABC=12x1y2-y3+x2y3-y1+x3y1-y2                  =12-3-7--8+-2-8-5+15--7                  =12-3+26+12                  =352square units

arACD=12x1y2-y3+x2y3-y1+x3y1-y2                  =12-3-8-3+13-5+65--8                  =1233-2+78                  =1092square units

∴ Area of the quadrilateral ABCD = 352+1092=1442=72 square units

Hence, the area of the given quadrilateral is 72 square units.

Mathematics
RD Sharma (2016)
Standard X

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