The area of an equilateral triangle with side $2 \sqrt{3} \, cm$ is (in $cm^2$):

The sides of a triangular plot are in the ratio of $4: 7: 9$ and its perimeter is $500 \, m$. Find its area.

$A$ rhombus shaped field has green grass for $18$ cows to graze. If each side of the rhombus is $30\, m$ and its longer diagonal is $48\, m$,how much area of grass field will each cow be getting (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.

Find the area of the triangle with the length of the sides $9 \, cm$,$10 \, cm$,and $17 \, cm$. (in $, cm^2$)

The sides of a triangle measure $20 \, cm$,$24 \, cm$,and $32 \, cm$. Find its semi-perimeter. (in $, cm$)