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 $DECB$?

In the given figure,triangle $ABC$ is drawn such that $AB$ is tangent to a circle at point $A$. The radius of the circle is $10 \, cm$. The line segment $BC$ passes through the center $O$ of the circle,and point $C$ lies on the circle. If $BC = 36 \, cm$ and $AB = 24 \, cm$,what is the area (in $cm^{2}$) of triangle $ABC$?

If the area of a triangle with base $x$ is equal to the area of a square with side $x,$ then the altitude of the triangle is

$A$ park square in shape has a $3 \, m$ wide road inside it running along its sides. The area occupied by the road is $1764 \, m^{2}$. What is the perimeter along the outer edge of the road? (in $metres$)

$A$ rectangular field costs $Rs. 110$ for levelling at $50$ $paise$ per square metre. If the ratio of length to breadth is $11: 5$, find the length of the field (in $m$).

How many tiles,each $4 \, dm$ square,will be required to cover the floor of a room $8 \, m$ long and $6 \, m$ broad?