#### Question

D, E, F, G are midpoints of sides of square ABCD. Given the areas of the three quadrilaterals, what is the area of the shaded one?

Question

Connect DF, EG, interesting at point GQ. Apparently, Q is the midpoint of DF and EG.

Connect OQ. So we get,

A_{ODQ}=A_{OFQ} in \triangle ODF,

A_{OEQ}=A_{OGQ} in \triangle OEG

Let T be the area of the square ABCD

A_{OFCG}+A_{ODBE}

=(\dfrac{1}{4}T+A_{OGQ}+A_{OFQ}) + (\dfrac{1}{4}T-A_{ODQ}-A_{OFQ})

=\dfrac{1}{2}T

=27+45

=73

Similarly,

A_{ODAG}+A_{OECF} = \dfrac{1}{2}T

A_{OECF} = \dfrac{1}{2}T - A_{ODAG}

=73-38

=35

Therefore, the area of the shaded region is 35 cm^2