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?
I know that the Theorem of Pythagoras, 3^2 + 4^2 = d^2. So I can find the radius with this and then .....?
If the rectangle is inscribed with all four corners touching the circle, then the diagonal of the rectangle is a diameter of the circle. Yes, use Phytagoras to find the diameter, then half that is the radius.
Yes, the the rectangle is inscribed with all four corners touching the circle. But my math isn't making sense to me.
Yes, the the rectangle is inscribed with all four corners touching the circle. But my math isn't making sense to me.
I know the steps I just cant compute
Ok, good start with 3^2 + 4^2 = c^2
then c = 5
Isn't that the diameter of the circle?
so the radius is 2.5
area of circle = pi(2.5)^2 =
area of rectang = 3*4 = 12
take the difference to find the shaded area.
To find the shaded area in the figure, you can follow these steps:
1. Start by using the dimensions of the rectangle inscribed in the circle (3 ft x 4 ft) to find the diameter of the circle.
- Use the Pythagorean theorem: 3^2 + 4^2 = d^2.
- Calculate the square root of the sum to find the diameter (d).
2. Once you have the diameter, divide it by 2 to find the radius (r).
3. Now that you have the radius, you can find the area of the circle using the formula A = π * r^2, where π (pi) is a constant approximately equal to 3.14159.
4. Next, calculate the area of the rectangle using its dimensions (length x width).
5. Subtract the area of the rectangle from the area of the circle to find the shaded area.
Let's go through an example:
1. According to the Pythagorean theorem, the diameter (d) of the circle is √(3^2 + 4^2) = √(9 + 16) = √25 = 5 ft.
2. The radius (r) of the circle is half of the diameter, so r = 5 ft / 2 = 2.5 ft.
3. The area of the circle is A = π * r^2 = 3.14159 * (2.5 ft)^2 = 3.14159 * 6.25 ft^2 ≈ 19.63 ft^2.
4. The area of the rectangle is A = length * width = 3 ft * 4 ft = 12 ft^2.
5. Finally, to find the shaded area, subtract the area of the rectangle from the area of the circle: 19.63 ft^2 - 12 ft^2 ≈ 7.63 ft^2.
Therefore, the shaded area in the figure is approximately 7.63 square feet.