Three equal circles, each of radius $6 \mathrm{cm}$ touch one another as shown in the figure. If the area enclosed between them is $k {\mathrm{cm}}^2$, then find the value of $k$. [Take $\pi =3.14$ and $\sqrt{3}=1.732$]

If three circles of radius $a$ each, are drawn such that each touches the other two, prove that the area included between them is equal to $\frac{4}{25}{a}^2$

[Take $\sqrt{3}=1.73$ and  $\pi =3.14$.]

 In the given figure, $ABCD$ is a trapezium of area $24.5 {\mathrm{cm}}^2$. If $AD\left|\right|BC$, $\angle DAB=90°, AD=10 \mathrm{cm}, BC=4 \mathrm{cm}$ and $ABE$ is quadrant of a circle then find the area of the shaded region in square centimetres.

$ABCD$ is a field in the shape of a trapezium, $AD\left|\right|BC$, $\angle ABC=90°$ and $\angle ADC=60°$. Four sectors are formed with centres $A, B, C$ and $D$, as shown in the figure. The radius of each sector is $14 \mathrm{m}$. If the total area of the four sectors is $x {\mathrm{m}}^2$, then find the value of $x$.

$ABCD$ is a field in the shape of a trapezium, $AD\left|\right|BC$, $\angle ABC=90°$ and $\angle ADC=60°$. Four sectors are formed with centres $A, B, C$ and $D$, as shown in the figure. The radius of each sector is $14 \mathrm{m}$. Find the following: area of the remaining portion in square metres, given that $AD=55 \mathrm{m}, BC=45 \mathrm{m}$ and $AB=30 \mathrm{m}$.

If the remaining area is $k {\mathrm{m}}^2$, find $k$

Find the area of the shaded region in the given figure in square centimetres, where a circular arc of radius $6 \mathrm{cm}$ has been drawn with vertex of an equilateral triangle of side $12 \mathrm{cm}$ as centre and a sector of circle of radius $6 \mathrm{cm}$ with centre $\mathrm{B}$ is made.

[Use $\sqrt{3}=1.73$ and $\pi =3.14$.]

In the given figure, $\mathrm{ABCD}$ is a rectangle with $\mathrm{AB}=80 \mathrm{cm}$and $\mathrm{BC}=70 \mathrm{cm}, \angle \mathrm{AED}={90}^{\mathrm{o}}$ and $\mathrm{DE}=42 \mathrm{cm}$. A semicircle is drawn, taking $\mathrm{BC}$ as diameter. Find the area of the shaded region in square centimetres.

In the given figure, from a rectangular region $\mathrm{ABCD}$ with $\mathrm{AB}=20 \mathrm{cm}$, a right triangle $\mathrm{AED}$ with $\mathrm{AE}=9 \mathrm{cm}$ and $\mathrm{DE}=12 \mathrm{cm}$, is cut off. On the other end, taking $\mathrm{BC}$ as diameter, a semicircle is added on outside the region: If the area of the shaded region is $k$ square centimetres up to two decimal places. then find the value of $k$.

[Use $\pi =3.14$]

In the given figure, $o$ is the centre of the circle with $\mathrm{AC}=24 \mathrm{cm}, \mathrm{AB}=7 \mathrm{cm}$ and $\angle \mathrm{BOD}=90°$. Find the area of shaded region in square centimetres.

[Use $\pi =3.14$]