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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.