$ABC$ is a triangle. $AB = 5 \text{ cm}$,$AC = \sqrt{41} \text{ cm}$,and $BC = 8 \text{ cm}$. $AD$ is perpendicular to $BC$. What is the area (in $\text{cm}^2$) of triangle $ABD$?

$ABCD$ is a parallelogram in which diagonals $AC$ and $BD$ intersect at $O$. If $E, F, G$ and $H$ are the midpoints of $AO, DO, CO$ and $BO$ respectively,then the ratio of the perimeter of the quadrilateral $EFGH$ to the perimeter of parallelogram $ABCD$ is

$A$ 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

$A$ bed of roses is shaped as shown in the figure below. In the centre is a square and on each side there is a semi-circle. The side of the square is $21 \, m$. If each rose plant needs $6 \, m^{2}$ of space,then the number of plants in the bed is?

One side of a parallelogram is $10\, m$ and the corresponding altitude is $7\, m$. The area of the parallelogram is......$m^2$

The diameter of a circular wheel is $7\, m$. How many revolutions will it make in travelling $22\, km$?