Q31 of 47 Page 1

Find the area of the quadrilateral whose vertices are A(3, 1), B(8, 1), C(7, 2) and D(5, 3).

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Given: A(3, 1), B(8, 1), C(7, 2) and D(5, 3).


By joining B to D, we will get two triangles ABD and BCD.


So, Area of quadrilateral ABCD = Area of ΔABD + Area of ΔBCD


We know that the area of Triangle = .


Now area of ΔABD = [3(1 – 3) + 8(3 – 1) + 5(1 – 1)]/2


= [3(-2) + 8(2) + 5(0)] / 2


= [-6 + 16] / 2


=10 / 2 = 5


∴ Area of ΔABD = 5 sq. Units


Also, area of ΔBCD = [8(2 – 3) + 7(3 – 1) + 5(1 – 2)]/2


= [8(-1) + 7(2) + 5(-1)]/2


= [-8 + 14 – 5]/2


= 1/2


∴ Area of ΔBCD = 0.5 sq units


So, Area of a quadrilateral = 5 + 0.5 = 5.5 sq. units


Ans. The area of quadrilateral is 5.5 sq. units.


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