A semi-circle and a circle with same radius inscribe a square of greatest possible area. What is the ratio of area of square inscribed by semicircle to that by circle?

In the following figure the radii (OA and OD) are $2 \mathrm{cm}$ and $∆\mathrm{ABO}$ and $∆\mathrm{DCO}$ are right-angle triangles. Also, $\mathrm{OB}=\sqrt{2} \mathrm{cm}$ and $\mathrm{OC}=1 \mathrm{cm}$. Find the area of the shaded region in the circle.

ABCD is a square of side $\mathrm{a} \mathrm{cm}$. ABBC,CD and AD all are the chords of circles with equal radii each. If the chords subtend an angle of $120°$ at their respective centres, find the total area of the given figure, where arcs are part of the circles :

ABCD and EFGA are the squares of side $4 \mathrm{cm}$, each. In square ABCD, DMB and PMQ are the arcs of circles with centers at A and C, respectively. In square AEFG, the shaded region is enclosed by two arcs of circles with centers at A and F, respectively. What is the ratio of the shaded regions of the squares ABCD and AEFG, respectively?