Circle $\mathrm{PQR}$ is inscribed in a quadrilateral $\mathrm{ABCD}$. The circle touches side $\mathrm{AD}$ at point $\mathrm{S}$. $\mathrm{AP}=8 \mathrm{cm}, \mathrm{QC}=3 \mathrm{cm}$ and $\mathrm{DC}=6 \mathrm{cm}$. The length of side $\mathrm{AD}$ is?

A regular hexagon is inscribed in an equilateral triangle, as shown. If the hexagon has an area of $12$, the area of this triangle is?

A ladder rests against a wall as shown. The top and the bottom ends of the ladder are marked $\mathrm{A}$ and $\mathrm{B}$. The base $\mathrm{B}$ slips. The central point $\mathrm{C}$ of the ladder falls along?

Square ABCD with side length $2$ is inscribed in a circle, as shown. Using each side of the square as a diameter, semicircular arcs are drawn. The area of the shaded region outside the circle and inside the semi-circular arcs are drawn. The area of the shaded region outside the circle and inside the semi-circle is?

The trapezoid shown has a height of length $12 \mathrm{cm}$, a base of length $16 \mathrm{cm}$, and an area of $162 {\mathrm{cm}}^2$. The perimeter of the trapezoid is?

In the diagram, each circle is divided into two equal areas and $\mathrm{O}$ is the centre of the larger circle. The area of the larger circle is $64\mathrm{\pi }$. The total area of the shaded regions is?

A ladybug wishes to travel from $\mathrm{B}$ to $\mathrm{A}$ on the surface of a wooden block with dimensions $2\times 4\times 8$ as shown in the diagram. Determine the shortest distance for the ladybug to walk.