The length of each side of an equilateral triangle having an area of $9 \sqrt{3} \text{ cm}^2$ is (in $\text{cm}$):

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

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

$A$ triangular park $ABC$ has sides $120\,m, 80\,m$ and $50\,m$ (see Fig.). $A$ gardener Dhania has to put a fence all around it and also plant grass inside. How much area does she need to plant? Find the cost of fencing it with barbed wire at the rate of $Rs. 20$ per metre leaving a space $3\,m$ wide for a gate on one side.

In a kite-shaped quadrilateral $ABCD$,$AB = AD = 12 \, cm$,$CB = CD = 17 \, cm$,and $AC = 25 \, cm$. Find its area and the length of diagonal $BD$.

The area of an equilateral triangle is equal to ............