For a rhombus plot,its perimeter is $680 \, m$ and one of its diagonals is $300 \, m$. Find the area of the plot. (in $, m^2$)

In quadrilateral $ABCD$, one of its diagonals $AC$ measures $20 \, cm$. The altitudes on $AC$ from vertices $B$ and $D$ are $8 \, cm$ and $12 \, cm$ respectively. Find the area of quadrilateral $ABCD$ in $cm^2$.

The sides of a quadrilateral $ABCD$ are $6 \, cm$,$8 \, cm$,$12 \, cm$,and $14 \, cm$ (taken in order) respectively,and the angle between the first two sides is a right angle. Find its area in $cm^2$.

The perimeter of an isosceles triangle is $32 \, cm$. The ratio of the equal side to its base is $3:2$. Find the area of the triangle.

$A$ plot,in the shape of a quadrilateral $XYZW$,has $XY = 25 \, m$,$YZ = 60 \, m$,$ZW = 33 \, m$,$WX = 34 \, m$,and $XZ = 65 \, m$. Find its area. (in $, m^2$)

Write True or False and justify your answer.
The area of an equilateral triangle is $20 \sqrt{3} \text{ cm}^2$ whose each side is $8 \text{ cm}$.