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

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

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.

$A$ 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).

$A$ rhombus shaped field has green grass for $18$ cows to graze. If each side of the rhombus is $30\, m$ and its longer diagonal is $48\, m$,how much area of grass field will each cow be getting (in $, m^{2}$)?