For a square with side length of 12 cm, draw a semicircle with the diameter of four sides. What is the area of the shadow part surrounded by these four arcs?

For a square with side length of 12 cm, draw a semicircle with the diameter of four sides. What is the area of the shadow part surrounded by these four arcs?

The area of the shadow part surrounded by the four arcs is the sum of the four semicircles minus the square area
A square with a side length of 12 cm has an area of 12 * 12 = 144 square cm
The semicircle has a diameter of 12cm, a radius of 6cm and an area of 6 * 6 * π / 2 = 18 π cm
The area of shadow part is 18 π * 4-144 = 72 π - 144 ≈ 82.08 square centimeter
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