Exercise A square with sides of length 2 has semicircles drawn on each side within the square. Find the total area of the shaded four petals.

Solution Assume the area of each petal is A1 and the area bounded by the side of the square and two adjacent petals is A2, then we have:

	2A1 + A2 = area of one semicircle	(1)
	4A1 + 4A2 = area of square	(2)

That is,

	2A1 + A2 = r² / 2 = /2	(3)
	4A1 + 4A2 = 2² = 4	(4)

(2) - 2 × (1):

	2A2 = 4 -
	A2 = 2 - /2	(5)

According to (3),

	2A1 = /2 - A2
	A1 = (/2 - A2)/2 = ( - 2)/2 = /2 - 1

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