Answer:
1. The area of the circle is 132.67 square centimeters
2. The area of the rectangle is 60 square centimeters
3. The area of the shaded region is 72.67 square centimeters
Explanation:
* Lets explain how to solve the problem
- A rectangle is inscribed in a circle, that means the vertices of the
rectangle lie on the circumference of the circle
∴ The diagonal of the rectangle = the diameter of the circle
- From the attached figure
∵ The diameter of the circle = 13 cm
∵ The radius of the circle is half the diameter
∴ The radius of the circle = 1/2 (13) = 6.5 cm
- The area of the circle = πr²
∵ π = 3.14
∴ The area of the circle = 3.14 × (6.5)² = 132.67 cm²
1. The area of the circle is 132.67 square centimeters
- The area of any rectangle = length × width
∵ The length of the rectangle is 12 cm
∵ The width of the rectangle is 5 cm
∴ The area of the rectangle = 12 × 5 = 60 cm²
2. The area of the rectangle is 60 square centimeters
- The area of the shaded region is the difference between the
area of the circle and the area of the rectangle
∵ The area of the circle = 132.67 cm²
∵ The area of the rectangle = 60 cm²
∵ The area of the shaded region = area of circle - area of rectangle
∴ The area of the shaded region = 132.67 - 60 = 72.67 cm²
3. The area of the shaded region is 72.67 square centimeters