ABCD is a square with area =625 in square. The circumfrence centered in circle is circunscribed by ABCD. Find the approximately value of the shaded area. Use pie = 3.14
I don't see any shaded area. The side length of the square is 25. The radius of the inscribed circle is 12.5. The difference in areas is
625 - pi(12.5)^2 = 134.1 in^2
= (1 - pi/4)*625
To find the approximate value of the shaded area, we need to determine the radius of the circumcircle and then subtract the area of the square from the area of the circle.
1. Start by finding the length of one side of the square (ABCD) since it is a square. Since the area of the square is given as 625 square units, we can calculate the length of one side by taking the square root of the area: √625 = 25.
2. Since the square is symmetric, the diagonal of the square can be used as the diameter of the circumcircle. Using the Pythagorean theorem, we can find the diagonal (d) of the square: d² = (length of one side)² + (length of one side)². Plugging in the values, we have d² = 25² + 25² = 625 + 625 = 1250. Taking the square root of 1250 gives us d ≈ 35.36.
3. The radius of the circumcircle is half the length of the diameter, so the radius (r) can be calculated as r ≈ d/2 = 35.36/2 ≈ 17.68.
4. Now we can find the area of the circle using the formula A = πr². Plugging in the value of π as 3.14 and the radius as 17.68, we have A = 3.14 * (17.68)² ≈ 982.77.
5. Finally, subtract the area of the square from the area of the circle to find the approximate value of the shaded area. Shaded Area ≈ Area of Circle - Area of Square ≈ 982.77 - 625 = 357.77 square units.
Therefore, the approximate value of the shaded area is 357.77 square units.