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Question

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

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Solution

Given: ABCD is a quadrilateral whose vertices are A(7,50,B(6,7),C(3,8) and D(2,3).
By joining AC, we get two triangles ABC and ADC
We know that:
Area of ΔABC=12[x1(y2y3)+x2(y3y1)+x3(y1y2)]
Area of triangle ABC:
=12[7(7(8)]+(6)[(8)5]+(3)[5(7)]
=12[7×(1)+(6)×(13)+(3)×12]
=12[7+7836]
=12×35=352 sq. units.
Area of triangle ADC.
=12[7(83)+(3)(35)+(2)(5(8)]
=12[(7)×(11)+(3)×(2)+2×13]
=12[77+6+26]=1092 sq. units.
Now, Area of quadrilateral PQRS=Area of triangle ABC+Area of triangle ADC
=35/2+109/2
=72 sq. units.

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