The image shows a problem asking to find the area of the shaded region inside a square. The square ABCD has a side length of 10 cm, and two quarter circles are drawn with centers at A and B, passing through D and C, respectively. The region inside the square but outside the quarter circles is shaded.

Steps to solve the problem:

1. Calculate the area of the square: The side of the square is given as 10 cm, so the area of the square is: $\text{Area of square} = 10^2 = 100 \, \text{cm}^2$

2. Calculate the area of each quarter circle: The radius of both quarter circles is equal to the side of the square, which is 10 cm. The area of a full circle with radius $r$ is $\pi r^2$, so the area of a quarter circle is: $\text{Area of one quarter circle} = \frac{\pi \times 10^2}{4} = 25\pi \, \text{cm}^2$

3. Find the area of the green shaded region: The shaded region is the part of the square outside the two quarter circles. Since the arcs intersect to form a smaller square in the center, we must subtract the area of the quarter circles from the total area of the square: $\text{Shaded area} = \text{Area of square} - 2 \times \text{Area of quarter circle}$ $\text{Shaded area} = 100 - 2 \times 25\pi$ Using $\pi \approx 3.14$: $\text{Shaded area} \approx 100 - 2 \times 78.5 = 100 - 157 = 36 \, \text{cm}^2$

Therefore, the area of the shaded region is 36 cm².

Final Answer:

The correct option is (b) 36 cm².

Do you have any questions, or would you like more details on any part of the solution?

Related Questions:

1. What is the perimeter of the square if the side length is 10 cm?
2. How would the shaded area change if the square had a different side length?
3. How do you calculate the area of a sector of a circle?
4. What is the total area covered by the two quarter circles?
5. How do you derive the formula for the area of a quarter circle?

Tip:

When dealing with geometric shapes involving circles and squares, always focus on understanding the relationships between areas and arcs, as this will make complex problems more manageable.