A chord of a circle of radius$20 \mathrm{cm}$sub tends an angle of $90°$at the center. Find the area of the corresponding major segment of the circle (Use $\pi =3.14$).

The radius of a circle with centre $\mathrm{O}$ is $5 \mathrm{cm}$. Two radii $\mathrm{OA}$ and $\mathrm{OB}$ are drawn at right angles to each other. Find the areas of the segments made by the chord $\mathrm{AB}$. $(\mathrm{\pi }=3.14)$. If the area of the minor segment is $\mathrm{p} {\mathrm{cm}}^2$, then find the value of $\mathrm{p}$.

$AB$ is the diameter of a circle, centre $O, C$ is a point on the circumference such that $\angle COB=\theta$. The area of the minor segment cut off by $AC$ is equal to twice the area of the sector $BOC$. Prove that  $\sin \frac{\theta }{2}\cos \frac{\theta }{2}$$=\pi$ $\left(\frac{1}{2}-\frac{\theta }{120}\right)$.

A chord of a circle subtends an angle of $\theta$ at the centre of the circle. The area of the minor segment cut off by the chord is one eighth of the area of the circle. Prove that $8$ $\sin \frac{\theta }{2}\cos \frac{\theta }{2}+\pi =\frac{\pi \theta }{45°}$.

A plot is in the form of a rectangle $\mathrm{ABCD}$ having a semi-circle on $\mathrm{BC}$ as shown in the following figure. If $\mathrm{AB}=60 \mathrm{m}$ and $\mathrm{BC}=28 \mathrm{m}$, find the area of the plot.

A play ground has the shape of a rectangle, with two semi-circles on its smaller sides as diameters, added to its outside. If the sides of the rectangle are $36 \mathrm{m}$ and $24.5 \mathrm{m}$, find the area of the playground. (Take $\mathrm{\pi }=\frac{22}{7}$)

Find the area of the circle in which a square of area $64$ ${\mathrm{cm}}^2$ is inscribed. [Use $\pi =3.14$]

A rectangular piece is$20 \mathrm{m}$ long and $15 \mathrm{m}$ wide. From its four corners, quadrants of radii $3.5 \mathrm{m}$ have been cut. Find the area of the remaining part.

In figure, $\mathrm{PQRS}$ is a square of side 4 $\mathrm{cm}$. Find the area of the shaded square.