in the middle circle have rectangle with length 12 and wide 5, find shaded area between rectangle and circle
what is the shaded area anyway???
the diagonal of the rectangle is the diameter of the circle: 13
So, the area between rectangle and circle is
π(13/2)^2 - 12*5 = 169π/4 - 60
To find the shaded area between the rectangle and the circle, we need to calculate the area of both shapes and subtract the area of the rectangle from the area of the circle.
1. Start by finding the area of the rectangle. We can use the formula for the area of a rectangle, which is length multiplied by width. In this case, the length is 12 and the width is 5, so the area of the rectangle is 12 * 5 = 60 square units.
2. Next, find the area of the circle. The formula for the area of a circle is π * r^2, where π is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle. However, to calculate the area of the shaded region, we need to find the area of the large circle and subtract the area of the rectangle.
3. To find the radius of the circle, we need to determine its diameter. From the given information, we know that the rectangle is inscribed within the circle, which means its diagonal should be the same as the diameter of the circle.
To calculate the diagonal of the rectangle, we can use the Pythagorean theorem. Since the rectangle is a right-angled triangle (width and length are the sides, diagonal is the hypotenuse), we have:
diagonal^2 = length^2 + width^2
diagonal^2 = 12^2 + 5^2
diagonal^2 = 144 + 25
diagonal^2 = 169
diagonal = √169
diagonal = 13
Therefore, the diameter of the circle is 13, and the radius is half of the diameter, which is 13/2 = 6.5.
4. Now, use the formula for the area of a circle to find the total area. The area of a circle is π * r^2. So, the area of the circle is 3.14159 * (6.5)^2 = 3.14159 * 42.25 ≈ 132.665 square units.
5. Finally, subtract the area of the rectangle from the area of the circle to find the shaded area. Shaded Area = Area of Circle - Area of Rectangle = 132.665 - 60 = 72.665 square units.
Therefore, the shaded area between the rectangle and the circle is approximately 72.665 square units.