In the given figure, a circle is inscribed in an equilateral triangle $ABC$ of side $12 \mathrm{cm}$. Find the radius of inscribed circle and the area of the shaded region in square centimetres. [Use $\sqrt{3}=1.73$ and $\pi =3.14$]. If $k {\mathrm{cm}}^2$ is the area of the shaded region, find $k$.

On a circular table cover of radius $42 \mathrm{cm}$, a design is formed by a girl leaving an equilateral triangle $ABC$ in the middle, as shown in the figure. Find the covered area of the design. [Use $\sqrt{3}=1.73$ and $\pi =\frac{22}{7}$.]

If the covered area is $k {\mathrm{cm}}^2$, find $k$.

A chord of a circle of radius $10 \mathrm{cm}$ subtends a right angle at the centre. If the area of the minor segment is $A {\mathrm{cm}}^2$, then find the value of $A$. [Use $\pi =3.14$]

The radius of a circular garden is $100 \mathrm{m}$. There is a road $10 \mathrm{m}$ wide, running all around it. Find the area of the road and the cost of levelling it at$₹20$ per ${\mathrm{m}}^2$ .

[Use $\pi =3.14$.]

If $₹k$ is the cost of levelling it, find $k$

The area of an equilateral triangle is $49\sqrt{3} {\mathrm{cm}}^2$. Taking each angular point as centre, circles are drawn with radius equal to half the length of the side of the triangle. Find the area of the triangle not included in the circles in square centimetres.

[Take $\sqrt{3}=1.73$, $\mathrm{\pi }=\frac{22}{7}$]

A child draws the figure of an aeroplane as shown. Here, the wings $ABCD$ and $FGHI$ are parallelograms, the tail $DEF$ is an isosceles triangle, the cockpit $CKI$ is a semicircle and $CDFI$ is a square. In the given figure, $BP\perp \mathrm{CD},$ $HQ\perp \mathrm{FI}$ and  $EL\perp DF$. IF $CD=8 \mathrm{cm},\mathit{ }BP=HQ=4 \mathrm{cm}$ and $DE=EF=5 \mathrm{cm}$, find the area of the whole figure in square centimetres. [Take $\pi =3.14$]

A circular disc of radius $6 \mathrm{cm}$ is divided into three sectors with central angles $90°, 120°$ and $150°$. What part of the whole circle is the sector with central angle $150°$? Also, Find the values of $l, m$ and $n$ if the ratio of the areas of the three sectors with central angles $90°, 120°$ and $150°$ is $l:m:n$ respectively. If  $k=\frac{n-m}{m-l}$, find $k$

A round table cover has six equal designs as shown in the given figure. If the radius of the cover is $35 \mathrm{cm}$ and the total area of the design is $k {\mathrm{cm}}^2$, then find the value of $k$. [Use $\sqrt{3}=1.732$, $\pi =3.14$ and write the final answer up to $1$ decimal places ]