In order to find the area of the shaded region, subtract the area of the smaler circle to the area of the bigger one.
A' = A2 - A1
A': total area
A2: bigger circle area
A1: smaller circle area
Use the formla for the area of the circle and replace the values of the radius of each circle, which can be obtained from the given diameters of the figure:
A2 = π r2²
r2 = d2/2 = 100mm/2 = 50 mm
A2 = π (50 mm)² = 7,853.98 mm²
A1 = π r1²
r1 = d1/2 = 80mm/2 = 40 mm
A1 = π (40 mm)² = 5,026.54
A' = 7,853.98 mm² - 5,026.54 mm²
A' = 2,827.43 mm²
Hence, the area of the shaded region is 2,827.43 mm²
