The image shows two circles, labeled $c_1$ and $c_2$, inside a rectangle. The rectangle has a height of 14 cm and a width of 26 cm. The task is to find the area of the shaded region (yellow) that lies outside the circles but inside the rectangle.

Step-by-step solution:

1. Calculate the area of the rectangle: $A_{\text{rectangle}} = \text{width} \times \text{height} = 26 \, \text{cm} \times 14 \, \text{cm} = 364 \, \text{cm}^2$

2. Determine the radius of the circles: Since the height of the rectangle is 14 cm and both circles fit perfectly within the height, the diameter of each circle is 14 cm. Therefore, the radius $r$ of each circle is: $r = \frac{14}{2} = 7 \, \text{cm}$

3. Calculate the area of one circle: The area $A_{\text{circle}}$ of a circle is given by the formula: $A_{\text{circle}} = \pi r^2 = \pi (7 \, \text{cm})^2 = 49\pi \, \text{cm}^2$ So, the area of one circle is approximately: $A_{\text{circle}} \approx 49 \times 3.1416 \approx 153.94 \, \text{cm}^2$

4. Calculate the total area of the two circles: Since there are two identical circles, the total area of the circles is: $A_{\text{total circles}} = 2 \times 153.94 \, \text{cm}^2 \approx 307.88 \, \text{cm}^2$

5. Calculate the shaded area: The shaded area is the area of the rectangle minus the total area of the circles: $A_{\text{shaded}} = A_{\text{rectangle}} - A_{\text{total circles}} = 364 \, \text{cm}^2 - 307.88 \, \text{cm}^2 \approx 56.12 \, \text{cm}^2$

Final Answer:

The shaded area is approximately 56.12 cm².

Would you like more details or have any questions? Here are some related questions:

1. How would the shaded area change if the circles were smaller?
2. What would be the formula to calculate the shaded area if there were three circles?
3. How does the formula for the area of a circle depend on its radius?
4. What happens to the shaded area if the rectangle's width increases but the circles remain the same?
5. How would you calculate the shaded area if the circles were not identical?

Tip: Always double-check the units when calculating areas, especially when combining different shapes.