a circle in inscribed in a rectangle. The rectangle measures 10 inches by four inches. Find the area of the shaded part
We cannot see the shaded part. If it is the circle, it will have a radius of 2 inches.
A = πr^2
If the shaded area is everything but the circle,
A = (10 * 4) - (πr^2)
To find the area of the shaded part, we need to determine the area of the rectangle and subtract the area of the inscribed circle.
The area of a rectangle is given by the formula: Area = Length × Width.
In this case, the length of the rectangle is 10 inches and the width is 4 inches.
So, the area of the rectangle is: 10 inches × 4 inches = 40 square inches.
To find the area of the inscribed circle, we need to know the radius of the circle. In an inscribed circle, the diameter of the circle is equal to the smaller side of the rectangle (in this case, 4 inches).
The formula for the area of a circle is: Area = π × Radius^2.
To find the area of the inscribed circle, we first need to find the radius. The radius of the circle is half of the diameter, so it will be: 4 inches / 2 = 2 inches.
Now, we can calculate the area of the inscribed circle: Area = π × (2 inches)^2 = 4π square inches.
Finally, to find the area of the shaded part, we subtract the area of the inscribed circle from the area of the rectangle:
Shaded Area = Area of Rectangle - Area of Circle
= 40 square inches - 4π square inches
This is the general formula for the shaded area. However, if you want the exact numerical value, you would replace π with its approximation of 3.14 or use a more precise value based on your needs.