According to Heron's formula,the area of a triangle $=$ ...........

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

Write True or False and justify your answer.
The area of a triangle with base $4 \, \text{cm}$ and height $6 \, \text{cm}$ is $24 \, \text{cm}^2$.

$A$ 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.

Find the area of a triangular field,two sides of which are $510\,m$ and $520\,m$ and the perimeter is $1560\,m$. Also,find the cost of the field at the rate of Rs. $21$ per $m^2$.

The triangular side walls of a flyover have been used for advertisements. The sides of the walls are $13 \, m$,$14 \, m$,and $15 \, m$. The advertisements yield an earning of $Rs \, 2000$ per $m^2$ a year. $A$ company hired one of its walls for $6$ months. How much rent did it pay? (in $Rs$)