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

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 $, cm^2$)

$A$ kite in the shape of a square with a diagonal $32\, cm$ and an isosceles triangle of base $8\, cm$ and sides $6\, cm$ each is to be made of three different shades as shown in the figure. How much paper of each shade has been used in it?

$A$ floral design on a floor is made up of $16$ tiles which are triangular,the sides of the triangle being $9\, cm, 28\, cm$ and $35\, cm$ (see Fig.). Find the cost of polishing the tiles at the rate of $50p$ per $cm^2$.

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?

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