$A$ traffic signal board,indicating '$SCHOOL$ $AHEAD$',is an equilateral triangle with side 'a'. Find the area of the signal board,using Heron's formula. If its perimeter is $180 \, cm$,what will be the area of the signal board?

There is a slide in a park. One of its side walls has been painted in some colour with a message "$KEEP$ $THE$ $PARK$ $GREEN$ $AND$ $CLEAN$". If the sides of the wall are $15 \, m$,$11 \, m$ and $6 \, m$,find the area painted in colour.

$A$ field is in the shape of a trapezium whose parallel sides are $25\, m$ and $10\, m$. The non-parallel sides are $14\, m$ and $13\, m$. Find the area of the field. (in $, m^{2}$)

Sides of a triangle are in the ratio of $12 : 17 : 25$ and its perimeter is $540 \, cm$. Find its area.

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 $, m^2$)?

An isosceles triangle has a perimeter of $30 \, cm$ and each of the equal sides is $12 \, cm$. Find the area of the triangle.