As shown in the diagram,$\triangle ABC$ is an equilateral triangle in which $BC = 70 \, cm$ and $P$ and $R$ are midpoints of $\overline{AB}$ and $\overline{AC}$ respectively. $\widehat{PQR}$ is an arc of $\odot(A, AP)$. Find the area of the shaded region. $(\sqrt{3} = 1.73)$ (in $cm^2$)

The length of the diagonals of a square garden $ABCD$ is $120\, m$. As shown in the figure,there are flower beds on two opposite sides of the garden in the shape of minor segments,the center of which is the point of intersection of the diagonals. Find the area of these flower beds. $(\pi=3.14)$ (in $m^2$)

The diameter of a circle with area $154\,cm^{2}$ is $\ldots \ldots \ldots . cm$.

As shown in the diagram,the side length of square garden $ABCD$ is $60\, m$. Flower beds are prepared in the shape of circular segments on two opposite sides of the square. The centre of the circles for these segments is the point of intersection $O$ of the diagonals of square $ABCD$. Find the total area of the two flower beds. (Use $\pi=3.14$) (in $m^2$)

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

If the sum of the areas of two circles with radii $R_{1}$ and $R_{2}$ is equal to the area of a circle of radius $R$,then