In the given figure, if $\mathrm{QRS}$ is an equilateral triangle and $\mathrm{TQS}$ is an isosceles triangle and $\mathrm{x}={47}^{\mathrm{o}}$, then the value of $\mathrm{y}$ (in degrees) will be:

$\mathrm{LMNOP}$ is semicircle with the centre $\mathrm{R}$ and diameter $\mathrm{LP}$. $\mathrm{LSR}$and $\mathrm{RQP}$ are also semicircles with centres at $\mathrm{T}$and $\mathrm{U}$, respectively, and diameters $\mathrm{LR}=\mathrm{RP}$ $=\frac{1}{ 2}$ $\mathrm{LP}$. The ratio of the perimeter of $\mathrm{LMNOP}$ and $\mathrm{LSRQP}$ is:

A goat is tied to two poles $\mathrm{P}$and $\mathrm{Q}$with ropes that are $15 \mathrm{m}$ long. $\mathrm{P}$and $\mathrm{Q}$are $20 \mathrm{m}$ apart as shown in the given diagram:

Which one of the following shaded portions indicates the total area over which the goat can graze?

In the given figure, all line segments of the shaded portion are of the same length and at right angles to each other. The same can be cut out on a board of side $10 \mathrm{cm}$. What is the area of the shaded portion?

In the figure given below, $\mathrm{ABCD}$ is a square of side length $4$units which has four symmetric cuts at all its corners. Find the area of the shaded portion.