$ABCD$ is a cyclic quadrilateral. $AB$ and $DC$ when produced meet at $P$. If $PA = 8 \ cm$,$PB = 6 \ cm$,and $PC = 4 \ cm$,then the length (in $cm$) of $PD$ is:

One side of a parallelogram is $10\, m$ and the corresponding altitude is $7\, m$. The area of the parallelogram is......$m^2$

The perimeter of a circle is equal to that of a square. Compare their areas.

What is the perimeter of an equilateral triangle whose area is $4 \sqrt{3} \text{ cm}^2$?

$A$ farmer wishes to start a $100 \, m^2$ rectangular vegetable garden. Since he has only $30 \, m$ of barbed wire,he fences three sides of the garden,using his house compound wall as the fourth side. The dimensions of the garden are:

The length of each side of an equilateral triangle is $12\, cm$. The height of the triangle is