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
Nmk, I've already solved this question for you in the previous message. Here are the final answers again for quick reference, using = 3.1: a) The shaded area is the area of the outer rectangle minus the area of the inner rectangle. Area_shaded = (10 cm × 6 cm) - (6 cm × 4 cm) = 60 cm^2 - 24 cm^2 = 36 cm^2 b) The shaded area is the sum of the rectangular part and the semicircular part. The rectangle is 12 cm × 12 cm, and the semicircle has a radius of 6 cm. Area_shaded = (12 cm × 12 cm) + (1)/(2) × 3.1 × (6 cm)^2 Area_shaded = 144 cm^2 + (1)/(2) × 3.1 × 36 cm^2 = 144 cm^2 + 55.8 cm^2 = 199.8 cm^2 c) The shaded area is the area of the square minus the area of the unshaded quarter circle. The square has a side length of 4 cm + 4 cm = 8 cm, and the quarter circle has a radius of 4 cm. Area_shaded = (8 cm)^2 - (1)/(4) × 3.1 × (4 cm)^2 Area_shaded = 64 cm^2 - (1)/(4) × 3.1 × 16 cm^2 = 64 cm^2 - 12.4 cm^2 = 51.6 cm^2 d) The shaded area is the area of the outer circle minus the area of the inner circle. The outer circle has a radius of 10 cm, and the inner circle has a radius of 5 cm. Area_shaded = (3.1 × (10 cm)^2) - (3.1 × (5 cm)^2) Area_shaded = (3.1 × 100 cm^2) - (3.1 × 25 cm^2) = 310 cm^2 - 77.5 cm^2 = 232.5 cm^2 3 done, 2 left today. You're making progress.