Find the area of the triangle with the side lengths $51 \, cm$,$52 \, cm$,and $101 \, cm$. (in $, cm^2$)

Find the area of the triangular field with the length of the sides $360 \, m$,$450 \, m$,and $450 \, m$.

$A$ field is shaped like an equilateral triangle. Its length is $120 \, m$ on each side. Calculate its area using Heron's formula.

$A$ field is in the shape of a trapezium having parallel sides $90 \, m$ and $30 \, m$. These sides meet the third side at right angles. The length of the fourth side is $100 \, m$. If it costs $\operatorname{Rs} 4$ to plough $1 \, m^2$ of the field,find the total cost of ploughing the field (in $\operatorname{Rs}$).

In a quadrilateral $ABCD$,$AB = 29 \, cm$,$BC = 35 \, cm$,$CD = 14 \, cm$,$DA = 50 \, cm$ and $AC = 48 \, cm$. Find its area. (in $, cm^2$)

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.