Areas of Shaded Regions | PDF - Free Printable

I will solve the problem by calculating the area of the shaded regions in both figures. I'll break this down step by step for each figure.

Figure 1:

This figure shows a square with two semicircles cut out from the top and bottom, leaving a shaded region in the middle.

Step 1: Calculate the area of the square
- The side length of the square is given as 10 cm.
- Area of square = side² = 10² = 100 cm²

Step 2: Calculate the area of the two semicircles
- Each semicircle has a diameter of 10 cm, so the radius is 5 cm.
- Two semicircles together form one complete circle.
- Area of circle = π × r² = π × 5² = 25π cm²

Step 3: Calculate the shaded area
- Shaded area = Area of square - Area of circle
- Shaded area = 100 - 25π cm²
- Using π ≈ 3.1416, this is approximately 100 - 78.54 = 21.46 cm²

Figure 2:

This figure shows a circle with a square inscribed inside it, and the shaded region is the area between the circle and the square.

Step 1: Calculate the area of the circle
- The radius of the circle is given as 7 m.
- Area of circle = π × r² = π × 7² = 49π m²

Step 2: Calculate the area of the inscribed square
- The diagonal of the square equals the diameter of the circle, which is 2 × 7 = 14 m.
- For a square with diagonal d, the side length s = d/√2 = 14/√2 = 7√2 m.
- Area of square = s² = (7√2)² = 49 × 2 = 98 m²

Step 3: Calculate the shaded area
- Shaded area = Area of circle - Area of square
- Shaded area = 49π - 98 m²
- Using π ≈ 3.1416, this is approximately 153.94 - 98 = 55.94 m²

Final Answers:

1. The area of the shaded region in Figure 1 is 100 - 25π cm² (approximately 21.46 cm²).
2. The area of the shaded region in Figure 2 is 49π - 98 m² (approximately 55.94 m²).