According to Heron's formula,the area of an equilateral triangle having each side $a$ is ..........

$A$ 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.

The shape of a plot is a rhombus. Its perimeter is $340 \, m$ and one diagonal is $72 \, m$. Find its area. (in $, m^2$)

Find the area of the triangular field with the length of the sides $360 \, m$,$450 \, m$,and $450 \, m$.

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

Find the area of the parallelogram given in the figure. Also,find the length of the altitude from vertex $A$ on the side $DC.$