Is every rectangle a parallelogram? Is every parallelogram a rectangle?

A rectangle with $12 \mathrm{cm}$ and $4 \mathrm{cm}$, reformed into a Rhombus. Both diagonals of Rhombus are equal and one of its angle is ${60}^{\mathrm{o}}$. Find the Area of Newly formed Rhombus.

Let $ABCD$ be a square. An arc of a circle with $A$ as centre and $AB$ as radius is drawn inside the square joining the points $B$ and $D$. Points $P$ on $AB, S$ on $AD, Q$ and $R$ on arc $BD$ are taken such that $PQRS$ is a square. Further suppose that $PQ$ and $RS$ are parallel to $AC$. Then, $\frac{\text{ area }PQRS}{\text{ area }ABCD}$ is

What is the area of this trapezoidal garden (All measurements are in cm)? 

1. $60$ sq.cm
2. $180$ sq.cm
3. $210$ sq.cm 
4. $240$ sq.cm

$5 : 18$ is the ratio of the length and perimeter of a rectangle. What would be the ratio of its length and breadth?

In the figure given below, a rectangle of perimeter $76$ units is divided into $7$ congruent rectangles:

What is the perimeter of each of the smaller rectangles?