$A$ 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?

Students of a school staged a rally for a cleanliness campaign. They walked through the lanes in two groups. One group walked through the lanes $AB, BC$ and $CA$; while the other through $AC, CD$ and $DA$ (see Fig.). Then they cleaned the area enclosed within their lanes. If $AB = 9 \, m, BC = 40 \, m, CD = 15 \, m, DA = 28 \, m$ and $\angle B = 90^{\circ}$,which group cleaned more area and by how much (in $, m^2$)? Find the total area cleaned by the students (neglecting the width of the lanes).

$A$ 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.

The sides of a triangular plot are in the ratio of $3 : 5 : 7$ and its perimeter is $300\, m$. Find its area.

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

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