$A$ 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 $Rs$).

The sides of a triangle are $6 \, cm$,$8 \, cm$,and $10 \, cm$. The area of the triangle is ............. $cm^{2}$.

The diagonals of a rhombus are $16\,cm$ and $30\,cm$. Find its perimeter. (in $,cm$)

In $\Delta ABC$,$AB = 6 \, cm$,$BC = 8 \, cm$,and $AC = 10 \, cm$. $BM$ is an altitude on $AC$. Then $BM = \dots \, cm$.

$A$ rectangular plot is given for constructing a house, having a measurement of $40 \, m$ long and $15 \, m$ in the front. According to the laws, a minimum of $3 \, m$ wide space should be left in the front and back each, and $2 \, m$ wide space on each of the other sides. Find the largest area where the house can be constructed (in $m^2$).

$A$ design is made on a rectangular tile of dimensions $50\, cm \times 70\, cm$ as shown in the figure. The design shows $8$ triangles,each with sides $26\, cm, 17\, cm$,and $25\, cm$. Find the total area of the design and the remaining area of the tile.