Area of a Circular Path or Area of a Ring

A horse is placed for grazing inside $70 \mathrm{m}$ by $52 \mathrm{m}$ and is tethered to one corner by a rope $21 \mathrm{m}$ long. Area can it gaze equals to $\mathrm{k} {\mathrm{metre}}^2$. Find the value of $\mathrm{k}$. Take $\pi =\frac{22}{7}$.

From a piece of cardboard, in the shape of a trapezium $\mathrm{ABCD}$, and $\mathrm{AB}\parallel \mathrm{CD}$ and $\angle \mathrm{BCD}=90°$, quarter circle is removed. Given $\mathrm{AB}=\mathrm{BC}=3.5 \mathrm{cm}$ and $\mathrm{DE}=2 \mathrm{cm}$. Calculate the area of the remaining piece of the cardboard. (Take $\mathrm{\pi }$ to be $\frac{22}{7}$)

Four equal circles, are described about the four corners of a square so that each circle touches two of the others. Find the area of the space enclosed between the circumferences of the circles, each side of the square measuring $24 \mathrm{cm}$. [Write answer up to $1$ decimal place and without units.] [Take $\pi =\frac{22}{7}$]

Four equal circles, each of radius $\text{'}a\text{'}$ touch one another. Find the value of $k$ if area between them is $\frac{k}{7}{a}^2$. Take $\pi =\frac{22}{7}$.

The area of an equilateral triangle is $49\sqrt{3} {\mathrm{cm}}^2$. Taking each angular point as a centre, a circle is described with a radius equal to half the length of the side of the triangle as shown in the figure. Find the area of the portion in the triangle not included in the circles. Write answer up to three decimal places without units. Take $\pi =\frac{22}{7}$.

In adjacent figure $\mathrm{A},\mathrm{B},\mathrm{C} \text{and }\mathrm{D}$ are centres of equal circles which touch externally in pairs and $\mathrm{ABCD}$ is a square of side $7 \mathrm{cm}$. Find the area of the region in between all the circles. Take $\pi =\frac{22}{7}$..

The adjacent figure consists of four half circles and two circles. If $\mathrm{OA}=\mathrm{OB}=\mathrm{OC}=\mathrm{OD}=14 \mathrm{cm}$. The area of the region $1+2+3+4$ is $\mathrm{k} {\mathrm{cm}}^2$. Find the value of $\mathrm{k}$. Take $\pi =\frac{22}{7}$.

The adjacent figure consists of four small semi-circles of equal radii and two big semi-circles of equal radii (each big semicircle diameter $42 \mathrm{cm}$). The area of shaded portion is $\mathrm{k} {\mathrm{cm}}^2$. Find the value of $\mathrm{k}$. Take $\pi =\frac{22}{7}$.

The area of a circle inscribed in a square of side $28 \mathrm{cm}$ is $\mathrm{k} {\mathrm{cm}}^2$. Find the value of $\mathrm{k}$.

[Hint: Diameter of the circle is equal to the side of the square, take $\mathrm{\pi }=\frac{22}{7}$]

A rectangular acrylic sheet is $36 \mathrm{cm} \text{by} 25 \mathrm{cm}$. From it, $56$ circular buttons, each of diameter $3.5 \mathrm{cm}$ have been cut out. The area of the remaining sheet is $\mathrm{k} {\mathrm{cm}}^2$. Find the value of $\mathrm{k}$. Take$\pi =\frac{22}{7}$ .