Area of right angled triangle $\Delta PQR$ 
$=\frac{1}{2}\times Base\times Height=\frac{1}{2}\times 5\sqrt{2}\times 5\sqrt{2}=25c{m}^2$

Area of right angled triangle $\Delta PSR$
$=\frac{1}{2}\times 8\times 6=24c{m}^2$

Area of quadrilateral PQRS
= Area of $\Delta PQR+\Delta PSR=49c{m}^2$

A soda can is a rough example of a cylinder.
The volume of a cylinder is $\pi r^{2}h$.
The capacity of any vessel is its internal volume so, the capacity of a soda can be calculated using the formula $\pi r^{2}h$.

Where,
r = base radius of the can

h = height of the can

Volume of cube = ${\left(edge\right)}^3$
Hence the volume of cube with edge 24 m is ${\left(24\right)}^3$
= 13824 $m^3$.

$\text{The area of a trapezium is given by:}$
$A=\frac{1}{2}\times \text{(Sum of parallel sides)}\times \text{(height)}$
$\Rightarrow 36=\frac{1}{2}\times (12+6)\times h$
$\Rightarrow h=4cm$
$\text{So now in the trapezium,}$​
$h=4cm$
$a=b=6cm$
$AB=CD\text{[S-A-S congruency in}△AFB\text{and}△DEC]$
$\therefore 2AB+a=12cm$
$\Rightarrow 2AB=12-6$
$\Rightarrow AB=CD=3cm$
$\text{So now in}△ABF,A{B}^2+h^2=d^2$​
$d^2=3^2+4^2=25$​
$d=5cm$
As the trapezium is isosceles, the slant sides of the trapezium are equal in length
$d=c=5cm$
$\therefore$ the perimeter of the trapezium
$=(2\times AB)+a+c+b+d$
$=(2\times 3)+6+5+6+5=6+22=28cm$

A cuboid whose length, breadth and height are equal is called a Cube. Cube is a special case of a cuboid in which all the sides are equal.

Let the radius of a cylinder be 'r' and the height of a cylinder be 'h'.
$\text{Volume of cylinder}=V=\pi r^{2}h\text{New radius}=2r\text{New height}=\frac{h}{2}\text{New volume}=\pi (2r{)}^2\frac{h}{2}=2\pi r^{2}h\text{New volume}=2V$