$A$ 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 $Rs$).

In quadrilateral $ABCD$,$AB = 20 \, cm$,$BC = 15 \, cm$,$CD = 12 \, cm$,$DA = 17 \, cm$ and $\angle B = 90^{\circ}$. Find the area of the quadrilateral in $cm^2$.

If each side of a triangle is doubled,then find the ratio of the area of the new triangle thus formed to the area of the given triangle.

The dimensions of a rectangle $ABCD$ are $51 \, cm \times 25 \, cm$. $A$ trapezium $PQCD$ with its parallel sides $QC$ and $PD$ in the ratio $9:8$ is cut off from the rectangle as shown in the figure. If the area of the trapezium $PQCD$ is $\frac{5}{6}$ th part of the area of the rectangle,find the lengths $QC$ and $PD$.

Area of a square $= \frac{(\ldots \ldots . .)^{2}}{2} .$

An isosceles triangle has a perimeter of $50\,cm$ and each of the equal sides is $17\,cm$. Find the area of the triangle. (in $,cm^2$)