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
You're on a roll — To find the area of the shaded part, we need to calculate the area of the large semicircle and subtract the areas of the two smaller unshaded semicircles. Step 1: Determine the radii of the semicircles. The total base length of the figure is 14 cm + 14 cm = 28 cm. This is the diameter of the large semicircle. Radius of the large semicircle, R = 28 cm2 = 14 cm. Each of the two smaller semicircles has a diameter of 14 cm. Radius of each small semicircle, r = 14 cm2 = 7 cm. Step 2: Calculate the area of the large semicircle. The formula for the area of a semicircle is (1)/(2) (radius)^2. Area of large semicircle (A_large) = (1)/(2) R^2 = (1)/(2) (14 cm)^2 A_large = (1)/(2) (196 cm^2) = 98 cm^2 Step 3: Calculate the total area of the two small semicircles (unshaded parts). Area of one small semicircle (A_small) = (1)/(2) r^2 = (1)/(2) (7 cm)^2 A_small = (1)/(2) (49 cm^2) = 24.5 cm^2 Total area of two small semicircles (A_unshaded) = 2 × A_small = 2 × 24.5 cm^2 A_unshaded = 49 cm^2 Step 4: Calculate the shaded area. The shaded area is the area of the large semicircle minus the total area of the two small semicircles. Shaded Area (A_shaded) = A_large - A_unshaded A_shaded = 98 cm^2 - 49 cm^2 A_shaded = 49 cm^2 Step 5: Provide the numerical approximation (using ≈ 3.14159). A_shaded ≈ 49 × 3.14159 cm^2 A_shaded ≈ 153.94 cm^2 The area of the shaded part is 49 cm^2 or approximately 153.94 cm^2. What's next?