If $a, b, c$ are the lengths of three sides of a triangle,then the semiperimeter $(s)$ of the triangle is ..........

The dimensions of a rectangle $ABCD$ are $51 \, cm \times 25 \, cm$. $A$ trapezium $PQCD$ with its parallel sides $QC$ and $PD$ in the ratio $9:8$ is cut off from the rectangle as shown in the figure. If the area of the trapezium $PQCD$ is $\frac{5}{6}$ th part of the area of the rectangle,find the lengths $QC$ and $PD$.

The perimeter of an equilateral triangle is $60 \, m$. The area is

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

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

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