For a triangle,$a = 15 \, cm$,$b = 20 \, cm$ and $s = 31 \, cm$,find the value of $c$.

If the sides of a triangular field are $290 \, m$,$290 \, m$,and $400 \, m$,find the area of the field in $m^2$.

In parallelogram $ABCD$,$AB = 9 \, cm$,$BC = 10 \, cm$ and $AC = 17 \, cm$,then find its area. (in $, cm^2$)

In quadrilateral $ABCD$, $\angle A = 90^{\circ}$, $AB = 15 \text{ cm}$, $BC = 25 \text{ cm}$, $CD = 12 \text{ cm}$, and $DA = 8 \text{ cm}$. Find the area of quadrilateral $ABCD$. (in $\text{ cm}^2$)

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

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 $s = \text{perimeter of triangle}$.