The maximum area of a triangle inscribed in a semicircle with diameter $50 \, cm$ is ........... $cm^{2}$.

In the figure, a circle of radius $7.5 \, cm$ is inscribed in a square. Find the area of the shaded region (Use $\pi = 3.14$) (in $cm^2$).

Sides of a triangular field are $15 \, m$,$16 \, m$,and $17 \, m$. At the three corners of the field,a cow,a buffalo,and a horse are tied separately with ropes of length $7 \, m$ each to graze in the field. Find the area of the field which cannot be grazed by the three animals.

Four circular cardboard pieces of radii $7 \, cm$ are placed on a paper in such a way that each piece touches the other two pieces. Find the area of the portion enclosed between these pieces (in $cm^2$).

The ratio of the areas of $\odot(O, 6)$ and $\odot(P, 12)$ is ...........

Is the area of the circle inscribed in a square of side $a \, cm$ equal to $\pi a^2 \, cm^2$? Give reasons for your answer.