To solve Question 14 from the image you provided, let's carefully read the problem and break it down step by step.

Problem Statement (Question 14):

The question reads:

In the figure, side of square = 4. What is the area of the non-shaded region?

From the figure in the image, we can see that there is a square and a shaded circular area inside it. The task is to find the area of the non-shaded region, which is the area of the square minus the area of the shaded circle.

Solution:

1. Identify Given Values:

   • Side length of the square, $s = 4$.

2. Calculate the Area of the Square: The area $A$ of a square is given by: $A_{\text{square}} = s^2$ Substituting the given side length: $A_{\text{square}} = 4^2 = 16$

3. Understand the Shaded Region (Circle): The shaded region is a circle inside the square. The diameter of the circle is equal to the side length of the square. Thus, the diameter $D$ of the circle is 4. The radius $r$ of the circle is half the diameter: $r = \frac{D}{2} = \frac{4}{2} = 2$

4. Calculate the Area of the Circle: The area $A$ of a circle is given by: $A_{\text{circle}} = \pi r^2$ Substituting the radius: $A_{\text{circle}} = \pi \times 2^2 = 4\pi$

5. Calculate the Area of the Non-Shaded Region: The non-shaded region is the area of the square minus the area of the circle: $A_{\text{non-shaded}} = A_{\text{square}} - A_{\text{circle}}$ Substituting the values: $A_{\text{non-shaded}} = 16 - 4\pi$

6. Final Answer: The area of the non-shaded region is $16 - 4\pi$.

Thus, the correct answer is 16 - 4π.

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

1. How do you calculate the circumference of a circle given its radius?
2. What would be the area of a square if its side length is doubled?
3. How do you calculate the area of a shaded region between two concentric circles?
4. What is the area of a triangle inscribed in a circle?
5. How does the area formula for regular polygons differ from that of a circle?

Tip: Remember that when working with circles, knowing either the radius or the diameter allows you to calculate both the circumference and area of the circle!