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

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).

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?

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

$A$ 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?