The diagonals of a square with area $9 {\mathrm{m}}^2$ divide the square into four non-overlapping triangles. What is the sum of the perimeter of the four triangles.

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

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?

In figure, $\mathrm{ABCD}$ is a parallelogram. Point$\mathrm{E}$ is on the ray $\mathrm{AB}$ such that $\mathrm{BE}=\mathrm{AB}$, then prove that line $\mathrm{ED}$ bisects segment $\mathrm{BC}$ at point $\mathrm{F}$.

Perimeter of a parallelogram is $150 \mathrm{cm}$. One of its sides is greater than the other side by $25 \mathrm{cm}$. Find the lengths of all sides.

In the figure, $\mathrm{PQRS}$ and $\mathrm{ABCR}$ are two parallelograms. If $\angle \mathrm{P} = 110°$ then, find the measures of all angles of $\mathrm{ABCR}$.

If the ratio of measures of two adjacent angles of a parallelogram is $1:2$, find the measures of all angles of the parallelogram.

Prove that quadrilateral formed by the intersection of angle bisectors of all angles of a parallelogram is a rectangle.