Answer :

More elaborated diagram is as shown below:


Area of quadrilateral = area(ABC) + area(ACD) …..(1)


Triangle ABC is a right triangle.


Therefore, area(ABC) =


=


=


=


Also, using Pythagoras theorem, we have:





Now we find that all sides of triangle ACD are equal.


i.e. AC = CD = AD = 20 cm


Therefore, triangle ACD is an equilateral triangle.


Area of equilateral triangle ACD =


=


= 173.2 sq. cm


Therefore, from (1), we get:


Area of quadrilateral = area(ABC) + area(ACD)


= 96 sq. cm+ 173.2 sq. cm


= 269.2 sq. cm


Hence, area of the quadrilateral is 269.2 square centimetres.


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