Find the area of the triangle inscribed in a circle circumscribed by a square made by joining the mid-points of the adjacent sides of a square of side $a$.

Find the sum of the areas of the shaded sectors given that $ABCDFE$ is any hexagon and all the circles are of same radius $r$ with different vertices of the hexagon as their centres as shown in the figure.

ABCD is a circle and circles are drawn with AO,CO, DO and OB as diameters.Areas E and F are shaded. E/F is equal to

The diagram shows six equal circles inscribed in equilateral triangle $ABC$. The circles touch externally among themselves and also touch the sides of the triangle. If the radius of each circle is $R$, area of the triangle is

A boy Mithilesh was playing with a square cardboard of side $2$ meters. While playing, he accidentally sliced off the corners of the cardboard in such a manner that a figure having all its sides equal was generated. The area of this eight-sided figure is: