Find the area of a triangle,two sides of which are $8 \, cm$ and $11 \, cm$ and the perimeter is $32 \, cm$.

$A$ field is shaped like an equilateral triangle. Its length is $120 \, m$ on each side. Calculate its area using Heron's formula.

If each side of a triangle is doubled,then find the ratio of the area of the new triangle thus formed to the area of the given triangle.

Sanya has a piece of land which is in the shape of a rhombus (see figure). She wants her one daughter and one son to work on the land and produce different crops. She divided the land into two equal parts. If the perimeter of the land is $400\, m$ and one of the diagonals is $160\, m$,how much area will each of them get for their crops (in $, m^2$)?

In $\Delta ABC$,$AB = 20 \, cm$,$BC = 48 \, cm$,and $AC = 52 \, cm$,find the area of $\Delta ABC$. (in $, cm^2$)

The lengths of the sides of a triangle are $13 \, cm$,$13 \, cm$,and $10 \, cm$. Find its area. Also,find the length of the altitude from the opposite vertex to the side whose length is $10 \, cm$.