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 $DECB$?

The perimeters of a circle,a square,and an equilateral triangle are the same,and their areas are $C$,$S$,and $T$ respectively. Which of the following statements is true?

In the adjacent figure,find the area of the shaded region in $cm^2$. (Use $\pi = 22/7$)

The sides of a triangle having area $7776 \ cm^2$ are in the ratio $3:4:5$. The perimeter of the triangle is ........ $cm$.

$A$ rectangular plot has a concrete path running in the middle of the plot parallel to the breadth of the plot. The rest of the plot is used as a lawn,which has an area of $240 \, m^2$. If the width of the path is $3 \, m$ and the length of the path is greater than its breadth by $2 \, m$,what is the area of the rectangular plot (in $m^2$)?

If the length of one side and the diagonal of a rectangle are $7 \text{ cm}$ and $25 \text{ cm}$ respectively,then find its perimeter (in $\text{cm}$).