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Question
Find the area of a quadrilateral ABCD whose vertices area A(3, -1), B(9, -5) C(14, 0) and D(9, 19).
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Solution
By joining A and C, we get two triangles ABC and ACD. Let
`A(x_1,y_1)=A(3,-1),B(x_2,y_2)=B(9,-5),C(x_3,y_3)=C(14,0) and D(x_4 , y_4 ) = D(9,19)`
Then,
`"Area of" ΔABC = 1/2 [ x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1 - y_2)]`
`=1/2 [ 3(-5-0) +9(0+1)+14(-1+5)]`
`=1/2 [-15+9+56] = 25` sq.units
`Area of ΔACD = 1/2 [ x_1 (y_3-y_4)+x_3(y_4-y_1)+x_4(y_1-y_3)]`
`=1/2 [ 3(0-19)+14(19+1)+9(-1-0)]`
`=1/2 [ -57 +280-9] = 107 sq. units`
So, the area of the quadrilateral is 25 +107 =132 sq . units.
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