$A$ 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?

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? $(1 \, \text{hectare} = 10000 \, m^2)$

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?

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.

Radha made a picture of an aeroplane with coloured paper as shown in the figure. Find the total area of the paper used. (in $, cm^{2}$)

Sanya has a piece of land which is in the shape of a rhombus (see figure). She wants her one daughter and one son to work on the land and produce different crops. She divided the land into two equal parts. If the perimeter of the land is $400\, m$ and one of the diagonals is $160\, m$,how much area will each of them get for their crops (in $, m^2$)?