Answer: The answer is 25 sq. units.
Step-by-step explanation: Given in the question five points A, B, C , D and E that lies on a circle. The common vertex 'I' lies on the three squares ABIG, MEIH and DKIL. The area of the squares ABIG and MEIH are 144 sq. units and 100 sq. units respectively. We are to find the area of square DKIL.
We can easily see in the given figure that the side of square DKIL is half of the side of square MEIH. So, we have
[tex]DL=\dfrac{1}{2}\times ME.[/tex]
Therefore, area of square DLIK will be one fourth of the area of square MEIH.
Hence, area of square DLIK is given by
[tex]a=\dfrac{1}{4}\times 100=25~\textup{sq. units}.[/tex]
Thus, the required area is 25 sq. units.
