The length of a rectangular field is double its width. Inside the field,there is a square-shaped pond $8 \, m$ long. If the area of the pond is $\frac{1}{8}$ of the area of the field,what is the length of the field? (in $m$)

Find the perimeter and area of the shaded portion of the adjoining diagram.

If the area of a square is equal to the area of a rectangle $6.4 \, m$ long and $2.5 \, m$ wide,then each side of the square measures (in $m$)

$A$ triangle and a parallelogram are constructed on the same base such that their areas are equal. If the altitude of the parallelogram is $100 \, m$,then the altitude of the triangle is

If the area of a triangle whose base is $6\, cm$ is equal to the area of a circle of radius $6\, cm$,then find the height of this triangle (in $cm$).

In $\triangle ABC,$ a line parallel to side $BC$ intersects sides $AB$ and $AC$ at points $D$ and $E$ respectively. Point $D$ divides $AB$ in the ratio $1:4.$ If the area of $\triangle ABC$ is $200 \text{ cm}^2,$ what is the area (in $\text{cm}^2$) of quadrilateral $DECB$?