If one angle of a parallelogram is a right angle, prove that it is a rectangle.

How many quadrilaterals are there in the given figure?

A circle is inscribed in quadrilateral ABCD, touching sides AB, BC, CD and DA at P, Q,R and S, respectively. If $\mathrm{As}=6\mathrm{cm},$ $\mathrm{BC}=12\mathrm{cm}$ and $\mathrm{CR}=5\mathrm{cm}$, then the length of AB (in cm) is

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?

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