Tick the correct answer in the following and justify your choice: If the perimeter and the area of a circle are numerically equal,then the radius of the circle is ......... $units$.

The area of an equilateral triangle $ABC$ is $17320.5 \, cm^2$. With each vertex of the triangle as a centre,a circle is drawn with a radius equal to half the length of the side of the triangle (see figure). Find the area of the shaded region in $cm^2$. (Use $\pi = 3.14$ and $\sqrt{3} = 1.73205$)

The side length of square $ABCD$ is $14 \, cm$. As shown in the diagram,circles with radius $7 \, cm$ are drawn with each vertex as the centre so that each circle touches two other circles externally. Find the area of the shaded region in $cm^2$.

The area of the circle that can be inscribed in a square of side $6 \, cm$ is (in $cm^2$) (in $\pi$)

Find the area of the shaded region given in the figure.

The areas of two sectors of two different circles with equal corresponding arc lengths are equal. Is this statement true? Why?