Write True or False and justify your answer.
If $a, b, c$ are the lengths of three sides of a triangle, then area of a triangle $= \sqrt{s(s-a)(s-b)(s-c)}$, where $s = \text{perimeter of triangle}$.

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?

According to Heron's formula,the area of a triangle $=$ ...........

If each side of a triangle is doubled,then find the ratio of the area of the new triangle thus formed to the area of the given triangle.

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

$A$ 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?