From the piece of cardboard, in the shape of a trapezium $ABCD$ and $AB\parallel DC$ and $\angle BCD={90}^{\circ }$, a quarter circle $\left(BFEC\right)$ with $C$ as its centre is removed. Given $AB=BC=3.5 cm$ and $DE=2 cm$, calculate the area of the remaining piece of the cardboard. ( Take $\mathrm{\pi }=\frac{22}{7}$)

The inside perimeter of a practice running track with semi-circular ends and straight parallel sides is $312 m$. The length of the straight portion of the track is $90 m$. If the track has a uniform width of $2 m$ throughout, find its area.

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