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 measure $12 \, cm$,$16 \, cm$,and $20 \, cm$. What is the area of the triangle in $cm^2$?

The perimeter of an isosceles triangle is $32 \, cm$. The ratio of the equal side to its base is $3: 2$. Find the area of the triangle.

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

The sides of a triangle are $a \, cm$,$b \, cm$,and $c \, cm$. Also,its semi-perimeter is $s \, cm$. If $s - a = 10 \, cm$,$s - b = 15 \, cm$,and $s - c = 12 \, cm$,then $s = \dots \, cm$.

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 $10.25 \, cm$.