On a piece of paper, four cardboard circles with radii of $7 \mathrm{cm}$ are arranged so that two of the circles touch each other. The region of the space bounded by these parts is

Join the centres of each circle to form a square.  By deducting the area occupied by the boxes on each circle from the total area of the built-up square, the necessary area—the space between the pieces—can be calculated.

The diameter of circle $=2\times 7=14 \mathrm{cm}$

So, the side of square is $14 \mathrm{cm}$.

Then area of square $={\mathrm{a}}^2=(14{)}^2=196{ \mathrm{cm}}^2$

Area of quadrant $=\frac{1}{4}\times$ area of circle

Area of space enclosed by the circles = Area of square of side $14 \mathrm{cm}-4$ (Area of quadrant of radius $7 \mathrm{cm}$ )

$={14}^2-4\times \frac{1}{4}\times \frac{22}{7}\times 7\times 7$

$=196-154$

$=42 {\text{cm}}^2$