The area of an equilateral triangle is $49\sqrt{3}{\mathrm{cm}}^2$. Taking each angular point as centre, a circle is described with 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.

Four equal circles, each of radius ‘$a$’ touch one another. Find the area between them.

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 $24 \mathrm{cm}.$

From a piece of cardboard, in the shape of a trapezium $ABCD,$ and $AB\left|\right|CD,$ and $\angle BCD = {90}^{°}$ 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$\frac{22}{7}$)

A horse is placed for grazing inside a rectangular field $70 \mathrm{m}$ by $52 \mathrm{m}$ and is tethered to one corner by a rope $21 \mathrm{m}$ long. How much area can it graze?