The diagram below is formed by 4 identical circles and a square. Each circle has a radius of 14 m. What is the area of the unshaded part? Take π as 3.14.

1. Break Down the Problem

To find the area of the unshaded part, we need to:

1. Calculate the area of the square.
2. Calculate the total area of the four identical circles.
3. Subtract the total area of the circles from the area of the square.

2. Relevant Concepts

• Area of a square: $A_{square} = (side)^2$
• Area of a circle: $A_{circle} = \pi r^2$ Where $r$ is the radius of the circle.

3. Analysis and Detail

1. Calculate the area of one circle: $A_{circle} = \pi r^2 = 3.14 \times (14)^2$ $= 3.14 \times 196 = 615.44 \, \text{m}^2$

2. Total area of four circles: $A_{total\_circles} = 4 \times A_{circle} = 4 \times 615.44 = 2461.76 \, \text{m}^2$

3. Determine the side length of the square: Since the circles are arranged such that their sides touch the sides of the square, the side length of the square will be double the radius of one circle: $side = 2 \times r = 2 \times 14 = 28 \, \text{m}$

4. Calculate the area of the square: $A_{square} = (side)^2 = (28)^2 = 784 \, \text{m}^2$

5. Calculate the area of the unshaded part: $A_{unshaded} = A_{square} - A_{total\_circles}$ $A_{unshaded} = 784 - 2461.76 = -1677.76 \, \text{m}^2$

4. Verify and Summarize

The calculations indicate that the area of the circles exceeds the area of the square. Hence, this suggests that either the arrangement or proportion of the shapes is not consistent with the description, as the unshaded part cannot be negative.

Final Answer

The calculated area of the unshaded part is negative, indicating an inconsistency in the question's premise.