A craftsman is crafting a square wooden plaque with a side length of 14 cm. A circular emblem is designed inside the plaque such that it touches all four of its edges. Find the area of the section of the square plaque that is not occupied by the circular emblem.

The correct answer is 42 cm².

Step 1: Calculate the area of the square plaque
The area of a square is given by the formula:
$\text{Area of square}={\text{side}}^2$
Given the side length of the square plaque, s = 14 cm:
$\text{Area of square}=14\times 14=196{\text{cm}}^2$

Step 2: Calculate the area of the circular emblem
Since the circular emblem touches all four edges of the square plaque, the diameter of the circle is equal to the side length of the square.
Diameter of the circle (d) = 14 cm
Radius of the circle (r):
$r=\frac{14}{2}=7\text{cm}$
The area of a circle is given by the formula:
$\text{Area of circle}=\pi r^2$
Using $\pi =\frac{22}{7}$:
$\text{Area of circle}=\frac{22}{7}\times 7^2=\frac{22}{7}\times 49=22\times 7=154{\text{cm}}^2$

Step 3: Calculate the area of the section not occupied by the circular emblem
The section of the plaque not occupied by the emblem is the difference between the total area of the square plaque and the area of the circular emblem:
$\text{Unoccupied area}=\text{Area of square}-\text{Area of circle}$
$\text{Unoccupied area}=196-154=42{\text{cm}}^2$

Thus, the area of the section of the square plaque that is not occupied by the circular emblem is 42 cm².