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Question

ABCD is a quadrilateral in which diagonal BD is perpendicular to the side AB. If AB=4.5 cm, AD=7.5 cm and the distance of C from BD is 1.5 cm, then find the area of quadrilateral.
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Solution

Consider the quadrilateral ABCD, such that diagonal BD is perpendicular to side AB and CM is the perpendicular to BD from C.
Also, we are given that AB=4.5cm;AD=7.5cm and CM=1.5cm
Now, the triangle ABD is a right angled triangle, by pythagoras theorem:
AB2+BD2=AD2
BD2=AD2AB2
=(7.5)2(4.5)2=56.2520.25=36=62
Area of ABD
A1=12×BD×AB since area=12×base×altitude.
A1=12×6×4.5=13.5cm2
Area of BCD
A2=12×BD×CM since area=12×base×altitude.
A2=12×6×1.5=4.5cm2
Now, area of the quadrilateral ABCD
=Area of ABD+Area of BCD
=A1+A2=(13.5+4.5)cm2=18cm2

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