Find the area of a quadrilateral $ABCD$ in which $AB = 3 \, cm, BC = 4 \, cm, CD = 4 \, cm, DA = 5 \, cm$ and $AC = 5 \, cm$. (in $, cm^2$)

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).

$A$ park,in the shape of a quadrilateral $ABCD$,has $\angle C = 90^{\circ}$,$AB = 9 \, m$,$BC = 12 \, m$,$CD = 5 \, m$,and $AD = 8 \, m$. How much area does it occupy (in $, m^{2}$)?

An umbrella is made by stitching $10$ triangular pieces of cloth of two different colours (see figure),each piece measuring $20\, cm, 50\, cm$ and $50\, cm$. How much cloth of each colour is required for the umbrella?

$A$ 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 $, m^{2}$)?

$A$ 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?