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Question

Find the area of a quadrilateral ABCD, the coordinates of whose vertices are A(3,2),B(5,4),C(7,6) and D(5,4).


Solution

|Area of triangle with vertices (x1,y1),(x2,y2) and (x3,y3)  is  given by 12|x1(y2y3)+x2(y3y1)+x3(y1y2)|

Area of quadrilateral ABCD= Area of triangle ABC+Area of triangle ADC

=12|3(4+6)+5(62)+7(24)|+12|3(4+6)5(62)+7(2+4)|
=12[|3(10)+5(8)+7(2)|+3(2)5(8)+7(6)|]
=12[|304014|+|6+40+42|]
=12[|84|+|76|]
=12[84+76]
=1602
=80 sq. units


Mathematics
RD Sharma
Standard X

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