The sides of a triangle measure $20 \, cm$,$24 \, cm$,and $32 \, cm$. Find its semi-perimeter. (in $, cm$)

Write True or False and justify your answer.
In a triangle,the sides are given as $11 \, cm$,$12 \, cm$,and $13 \, cm$. The length of the altitude corresponding to the side of length $12 \, cm$ is $10.25 \, cm$.

An isosceles right triangle has an area of $8 \, cm^{2}$. The length of its hypotenuse is

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

In quadrilateral $ABCD$,$AB = 9 \, cm$,$BC = 13 \, cm$,$CD = 14 \, cm$,$DA = 12 \, cm$,and $BD = 15 \, cm$. Find the area of quadrilateral $ABCD$ in $cm^2$.

The sides of a triangle are $35 \text{ cm}$,$54 \text{ cm}$,and $61 \text{ cm}$,respectively. The length of its longest altitude is: