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In this question all lengths are in centimetres and all angles are in radians. A- B C r. F EST The diagram shows the rectangle ADEF, where AF = DE = r. The points B and C lie on AD such that AB = CD = r. The curve BC is an arc of the circle, centre O, radius r and has a length of 1.5r. (a) Show that the perimeter of the shaded region is (7.5 + 2sin 0.75)r. [5] (b) Find the area of the shaded region, giving your answer in the form kr², where k is a constant correct to 2 decimal places. [4]
