Find the area of a triangle two sides of which are $18 \, cm$ and $10 \, cm$ and the perimeter is $42 \, cm$.

$A$ 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 $cm^2$.

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

Kamla has a triangular field with sides $240 \, m, 200 \, m, 360 \, m$,where she grew wheat. In another triangular field with sides $240 \, m, 320 \, m, 400 \, m$ adjacent to the previous field,she wanted to grow potatoes and onions. She divided the field in two parts by joining the mid-point of the longest side to the opposite vertex and grew potatoes in one part and onions in the other part. How much area (in hectares) has been used for wheat,potatoes and onions? $(1 \, \text{hectare} = 10000 \, m^2)$

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).

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.