In the figure given below, $AOB$ is a sector of angle $60°$ of a circle with centre $O$ and radius $17 \mathrm{cm}$. If $AP\perp OB$ and $AP=15 \mathrm{cm}$, find the area of the shaded region. $(\text{Use} x=3.14)$

In the following figure, a square is inscribed in a circle of diameter $d$. Is the area of the outer square four times the area of the inner square? Give reasons for your answer.

The side of a square is $10 \mathrm{cm}$. Find the area between circumscribed and inscribed circles of the square.

In the figure given below, $ABCD$ is a rectangle with $AB=80 \mathrm{cm} \text{and} BC=70 \mathrm{cm}$. If $\angle AED=90°$, $DE=42 \mathrm{cm}$ and a semicircle is drawn with $BC$ as diameter, find the area of the shaded region.

Find the perimeter and area of the shaded region in figure given below.

A momento is made as shown in figure given below. Its base $PBCR$ is silver plated from the front side. Find the area which is silver plated.

Given below, arcs are drawn by taking vertices $A, B \text{and} C$ of an equilateral triangle of side $14 \mathrm{cm}$ to intersect the sides $BC, CA \text{and} AB$ at their mid-points $D, E \text{and} F$ respectively. Find the area of the shaded region.