This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
The figure shows a circle with an inscribed square. The shaded part is the area of the circle minus the area of the inscribed square. Step 1: Identify the dimensions of the circle and the square. The given length of 21 cm is the diagonal of the inscribed square and also the diameter of the circle. So, the diameter of the circle d = 21 cm. The radius of the circle r = (d)/(2) = (21)/(2) cm. For the inscribed square, its diagonal D = 21 cm. We are given = (22)/(7). Step 2: Calculate the area of the circle. The formula for the area of a circle is A_c = r^2. A_c = (22)/(7) × ((21)/(2))^2 A_c = (22)/(7) × (21 × 21)/(2 × 2) A_c = (22)/(7) × (441)/(4) A_c = (22 × 441)/(28) A_c = (11 × 441)/(14) A_c = (4851)/(14) A_c = 346.5 cm^2 Step 3: Calculate the area of the inscribed square. The formula for the area of a square using its diagonal D is A_s = (1)/(2)D^2. A_s = (1)/(2) (21)^2 A_s = (1)/(2) (441) A_s = (441)/(2) A_s = 220.5 cm^2 Step 4: Calculate the area of the shaded part. The area of the shaded part is the area of the circle minus the area of the square. Shaded Area = A_c - A_s Shaded Area = 346.5 cm^2 - 220.5 cm^2 Shaded Area = 126 cm^2 The area of the shaded part is 126 cm^2. 3 done, 2 left today. You're making progress.