Find the shaded area in the following figure if the rectangle inscribed in the circle has dimensions 3 ft x 4 ft.
I know I find the area of the rectangle A=l*w, but what do I do next?
Don't know until we know what is shaded.
To find the shaded area, you need to subtract the area of the rectangle from the area of the circle. Here are the steps to do that:
1. Find the area of the rectangle: Since the dimensions of the rectangle are given as 3 ft x 4 ft, you can use the formula for the area of a rectangle, which is A = length × width. In this case, A = 3 ft × 4 ft = 12 square feet.
2. Find the area of the circle: The formula for the area of a circle is A = πr², where π is a constant approximately equal to 3.14, and r is the radius of the circle. In this case, you don't have the radius directly, but you know that the rectangle is inscribed in the circle. That means the diameter of the circle is equal to the length of the rectangle. Since the length of the rectangle is 4 ft, the diameter of the circle is also 4 ft. Therefore, the radius is half of the diameter, which is 4 ft ÷ 2 = 2 ft. Now you can use the formula to calculate the area of the circle: A = 3.14 × (2 ft)² ≈ 12.56 square feet.
3. Subtract the area of the rectangle from the area of the circle: To find the shaded area, you need to subtract the area of the rectangle (12 square feet) from the area of the circle (approximately 12.56 square feet). So, the shaded area is 12.56 square feet - 12 square feet = 0.56 square feet.
Therefore, the shaded area in the figure is approximately 0.56 square feet.