In quadrilateral $ABCD$,$AB = 40 \, cm$,$BC = 35 \, cm$,$CD = 48 \, cm$,$DA = 29 \, cm$ and $BD = 29 \, cm$. Find the area of quadrilateral $ABCD$. (in $, cm^2$)

In quadrilateral $ABCD$, one of its diagonals $AC$ measures $20 \, cm$. The altitudes on $AC$ from vertices $B$ and $D$ are $8 \, cm$ and $12 \, cm$ respectively. Find the area of quadrilateral $ABCD$ in $cm^2$.

$\Delta ABC$ is an isosceles triangle in which $BC = 24 \, cm$ and $AB = AC = 13 \, cm$. Then,the area of $\Delta ABC = \dots \, cm^2$.

State whether each of the following statements is true or false:
$(1)$ In a square,if the length of each side is $20 \, cm$,then the length of its diagonal is $20 \sqrt{2} \, cm$.
$(2)$ If each side of an equilateral triangle is doubled,the area of the triangle is twice the area of the original triangle.

$A$ rhombus-shaped sheet with a perimeter of $40 \, cm$ and one diagonal of $12 \, cm$ is painted on both sides at the rate of $Rs \, 5$ per $cm^2$. Find the cost of painting (in $Rs$).

Area of a rectangle $=$ ............