Areas of Sector and Segment of a Circle

A triangular field, having grass, has sides $20 \mathrm{m}, 34 \mathrm{m} \text{and} 42 \mathrm{m}$ respectively. Three horses are tied to each of the vertices with a rope of length $7 \mathrm{m}$. each. The horses start grazing the field. The area of the portion of the field that is ungrazed by the horses is_____${\mathrm{m}}^2$.

In the given figure, $ABCPA$ is a quadrant of a circle of radius $14cm$. With $AC$ as diameter, a semi-circle is drawn. The area of the shaded region is

Three horses are tethered with $7$ metre long ropes at the three corners at a triangle field having sides $20m$ , $34m$ and $42m$ . The area of the plot which can be grazed by horses is:

In the given figure, the centre of the circle is $A$ and $ABCDEF$ is a regular hexagon of side $6\mathrm{cm}$. The approximate area of segment $BPF$ is (Take $\mathrm{\pi }=3.14$)

The length of the minute hand of a clock is $14$ $\mathrm{c}\mathrm{m}.$ The area swept by the minute hand in $5$ minutes is

In the figure a semicircle with centre $‘O’$ is drawn on $AB$. If $\angle ABP = 60°$ then the ratio of area of larger region to area of smaller shaded region is

Length of Minute hand of a clock is $14$ cm. Area [In ${\text{cm}}^2$] formed by this hand in $5$ minutes is  [Take $\mathrm{\pi }=\frac{22}{7}$]

The length of a minute hand of a clock is $6$cm. What will be the area(approximate) of the sector swept by this minute hand with in $45$ minutes.

The time taken by the minute hand of a watch to describe an angle of $\frac{3}{4}\mathrm{\pi }$ radians is

A momento is made as shown in the figure. Its base $PBCQ$ is silver plated from the front side.

The silver plated area is (use $\mathrm{\pi }=\frac{22}{7}$)

ABC is an equilateral triangle. Find the area of the shaded region if the radius of each of the circle is $1 cm$.

A semicircle with $AB$ as diameter is drawn. $C$ is a point on semi circle such that arc$\stackrel{⏜}{AC}$ and $\stackrel{⏜}{CB}$ are congruent. $D$ is the midpoint of the chord $AC.$ Find the area of the shaded region.

If $PQ=QR=RS$ and four semicircles are drawn with $PS, QR, PR, QS$ as a diameter. Find the values of $\frac{A_1+A_3}{A_4+A_2}=?$
 

Find the length of arc DE if the centroid of equilateral $△ABC$ lies on a circle drawn with B as a centre and BF $=6$ units.

O is the centre of the semicircle and C is the centre of the quarter circle. If $CO=1,$ find the area of the shaded region.

If P and S are the centre of quarter circles and $C_1, C_2$ and $C_3$ are the centre of semicircles $A_1, A_2, A_3$ and $A_4$ repressions the areas as shown in the diagrams, then

Side AB of square ABCD is the diameter of semicircle drawn as per diagram. A quarter circle is drawn with D as a centre. Find $x$ if the difference of areas of the two shaded regions is $18\mathrm{\pi } {\mathrm{cm}}^2.$

PQR are centres of arcs drawn passing through centre O is the bigger circle. What is the area of shaded region if $\stackrel{⏜}{PQ}$, $\stackrel{⏜}{QR}$ and $\stackrel{⏜}{RP}$ are congruent?

Arcs are drawn by taking every vertex of Hexagon as centre. If the smallest diagonal is $6$ cm, then find the perimeter of the shaded region.

 

 If P, Q represents the area of sectors, OC$=$CD  and $\angle$AOB$=\angle$COD. Then find the ratio of $P$ and $Q$.