Find the area of the equilateral triangle having length of each side $50\, cm$.

Write True or False and justify your answer.
In a triangle,the sides are given as $11 \, cm$,$12 \, cm$,and $13 \, cm$. The length of the altitude corresponding to the side of length $12 \, cm$ is $10.25 \, cm$.

Find the area of a triangle,two sides of which are $15\,cm$ and $28\,cm$ and the perimeter is $84\,cm$. (in $,cm^2$)

In quadrilateral $ABCD$,$AB = 40 \, cm$,$BC = 35 \, cm$,$CD = 48 \, cm$,$DA = 29 \, cm$ and $BD = 29 \, cm$. Find the area of quadrilateral $ABCD$. (in $, cm^2$)

$A$ 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 $Rs$).

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