Height of an equilateral triangle is $9 \ cm$. Find its area?

What is the area of the shaded portion if each side of the square measures $21\,cm$? (in $cm^2$)

In $\Delta ABC$,$AD$ and $AE$ are bisectors of $\angle BAC$ and $\angle BAD$ respectively. If $\angle BAE = 30^{\circ}$,$AE = 9 \text{ cm}$,and $EC = 15 \text{ cm}$,what is the area (in $\text{cm}^2$) of $\Delta AEC$?

$A$ rectangular plot has a concrete path running in the middle of the plot parallel to the breadth of the plot. The rest of the plot is used as a lawn,which has an area of $240 \, m^2$. If the width of the path is $3 \, m$ and the length of the path is greater than its breadth by $2 \, m$,what is the area of the rectangular plot (in $m^2$)?

$A$ rectangular carpet has an area of $60 \, m^{2}$. Its diagonal and longer side together equal $5$ times the shorter side. The length of the carpet is.........$m$

$A$ playground is in the shape of a rectangle. $A$ sum of ₹ $1,000$ was spent to make the ground usable at the rate of $25$ $paisa$ per $m^2$. The breadth of the ground is $50\, m$. If the length of the ground is increased by $20\, m$,what will be the expenditure in rupees at the same rate per $m^2$?