In a quadrilateral $ABCD$,the sides $AB, BC, CD, DA$ measure $20\, m, 13\, m, 17\, m$ and $10\, m$ respectively,and the diagonal $AC$ is $21\, m$. The area of the quadrilateral is ........ $m^2$.

The breadth of a rectangular plot is $75 \%$ of its length. If the perimeter of the plot is $1050 \, m,$ what is its area (in $, m^2$)?

In the figure,$DE \parallel BC$. If $DE = 3 \text{ cm}$,$BC = 6 \text{ cm}$,and the area of $\Delta ADE = 15 \text{ cm}^2$,then the area of $\Delta ABC$ is ............ $\text{cm}^2$.

$ABCD$ 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

Among a square of perimeter $44\, cm$ and a circle of circumference $44\, cm,$ which figure has a larger area and by how much?

What is the area of a given right-angled triangle?
$I.$ The length of the hypotenuse is $5\, cm$.
$II.$ The perimeter of the triangle is four times that of its base.
$III.$ One of the angles of the triangle is $60^{\circ}$.